There are several veteran gamers who've complained about how 4th Edition D&D has become more reliant on miniatures. Imagine my surprise when this was confirmed by browsing through the Dungeon Master's Guide: it lists D&D Miniatures as "What You Need to Play". Of course I'd like to qualify that statement. I don't think the current edition of D&D is reliant in miniatures. It has, however, become more reliant on the battle grip or a map (this is either more retro-D&D for you or a slight increase in reliance if your basis is D&D 3.X). What's the difference? Well, honestly, you don't need miniatures for the game. If spending money is a concern for you, you can simply use tokens, counters, or markers to represent your PCs and the monsters you're facing. (You can check out Fiery Dragon's free PDF of counters for use in Keep of the Shadowfell.) The battle grid, on the other hand, reflects the tactical aspects injected into the game.
The first nuance of the game is the decision to stick to 1-inch squares. Now many tactically-oriented gamers will praise the value of hex-based maps. To avoid a long discussion on the matter, I'll simply agree with the superiority of hex-based maps. However, there's one advantage 1-inch squares have over hexes: they're simpler to create. If I were to make my own D&D map, it's really as simple as getting a ruler and a marker. Squares are easier to draw than hexagons, especially when you're in a rush. And D&D 4E is a game where you might want to create your own maps as well as take advantage of the various products out there (whether it's Dungeon Tiles or third-party maps). I'll explain below how to take advantage of the terrain.
The second nuance of the game is simplifying movement, especially consistently counting diagonals as one square. This honestly sped up our game as our PCs moved into optimal positions and it was simple as counting 1, 2, 3, 4, 5 (or in the case of one player, 5, 10, 15, 20). That's not to say opposition to movement still isn't there. There's Difficult Terrain for example which counts as 2 squares. The departure from the 3.X movement rules however has avoided questions like "how much movement is it costing me to travel diagonally twice over Difficult Terrain?". Also, the addition of push/pull/slide effects might complicate matters if you do use the "every other diagonal costs 2 squares" rule. I mean what happens if you choose to slide an opponent two squares diagonally? Is that possible? Thankfully, the simplification of the rules avoids this type of questions. And if it's game balance that you're concerned about, just remember this: everyone (PCs or Monsters) can move diagonally without penalties, so it's an even playing field!
The third nuance of the game are the push/pull/slide effects. When I first read the rules, the inclusion of such effects baffled me. I mean why bother? My first impression was that such effects would be limited to creating flanking maneuvers. After running the game however, I discovered I was wrong. The push/pull/slide effects leads to interesting tactical situations not apparent until you play the game. For example, there was one scenario when the party's Fighter and Paladin charged a pack of wolves. Thanks to initiative and some smart movements on my part, I eventually surrounded them to the point that I even knocked one of the PCs unconscious. Now in 3.X, if you're surrounded on all adjacent sides, there's not really much else you can do aside from killing one of your opponents and making a break for it. In this edition of the game, the party's Rogue and Warlord eventually broke through the "wall of wolves" to rescue their teammates as well as creating flanking and tactically-superior maneuvers (i.e. placing the wolves in Difficult Terrain, pushing them to one side, etc.). Push/pull/slide have given the game an extra layer of depth that's not readily apparent but will keep combat interesting even if you're fighting kobolds for the nth time.
The fourth nuance of the game is that terrain actually matters now. It can be a table in a bar, bushes in the wilderness, or a coffin in a dungeon. This is why you want to create your own maps or even use third-party maps as is: because the details matter. Between the push/pull/slide effects, the various terrain effects (Difficult Terrain, Blocking Terrain, Challenging Terrain, Obscuring Terrain, etc.), and Traps/Hazards, the lay of the land matters. Want to jump over the bar table to reach the goblin at the other end? Make an Athletics/Acrobatics check to do so. How about that Brute charging the party's Wizard? Push them into that wilderness where they'll slow to a crawl! Oh, and that coffin you're standing beside? It's a trigger for those flying darts! D&D 4E can be Iron Heroes or Tomb of Horrors, depending on your play style. Moreover, those random details in maps start to matter. Don't remove them, work with them!
Fifth, because of the emphasis on larger and bigger maps, ranged attackers start to matter again. I mean when I was playing 3.X, if anyone was playing a ranged character, any opponent could probably get to them in a charge. Aside from that, they were reduced to 5-ft. steps and then shooting. Here, ranged attackers (either on the side of the players or the GM) start to matter again. Finding a tactically safe position to fire from afar is a viable method in the game, just as artificially holding off the attackers from the party's Wizard or Ranger thanks to the Defenders. The terrain features also add options to the game, whether for ranged attackers (i.e. Difficult Terrain) or against them (i.e. Obscuring Terrain). Melee fighters must also choose their abilities wisely as their attacks can help their allies (pushing an enemy into the line of fire) or hinder them (tripping the enemy gives the ranged attacker penalties to hit).
Let's wrap things up by combining all of these elements into a concrete example. Let's say you're using a chessboard as a battle grid (come on, you know you always wanted to run that chess-based dungeon; see Dragon Magazine #358 for ideas). The PCs are on one side and the Monsters are on the other. The simplest, and perhaps most boring method, is to have the squares have no impact on the game. But let's see what kind of games we can run by changing all the black squares. If we assume all the black squares are Difficult Terrain, then it suddenly slightly becomes more difficult to get to the ranged attackers in each party. Also, this encourages diagonal movement for the melee attackers as passing through white squares is the optimum choice when it comes to movement. The Warlord and the Rogue on the other hand, both of which have abilities to slide and/or move before/after the attack, might move through those black squares to catch enemies unaware. Change the black squares to Blocking Terrain and suddenly the ranged attackers are at a disadvantage as many of their opponents aren't in their line of sight or have cover at the very least. Melee characters or the Wizard will be able to block off certain parts of the terrain completely, isolating monsters or "herding" them into the line of fire. Switching the black squares to Challenging terrain (i.e. skill checks are needed) shuffles things again. Lightly-armored and skilled characters might gamble on the black squares while heavily-armored characters will most likely travel through white squares. Ranged attackers again are at an advantage in this set-up, but it's not always as clear-cut, especially if you mix it up with Obscuring terrain. You could even include Hazards, Traps, or simply alternate effects (Blocking Terrain simply shifts to Challenging Terrain, either every other round or at odd numbers in the initiative track) to produce a diverse set of effects.
That's not to say you couldn't do all of this in previous editions of the game but with more defined roles (i.e. The Fighter impedes opponents from moving away from him, the Warlord able to slide and move allies into other squares, etc.) and rules that support this style of play (it's explicitly written in the Dungeon Master's Guide), the terrain and tactical movement starts to matter more and opens up new strategies for the game.