First, it makes it a lot easier to remember who is where doing what. Most people are visually oriented, and actually seeing something allows them to picture it better and understand it better.
Second, it avoids misunderstandings, verbal blunders, etc - "I thought you said that door was FIFTEEN feet down the hall, not FIFTY."
Or..."The hallway before you stretches about 50' south. On the west wall are two doors, each 10' apart, starting 20' into the hallway. Another hallway appears to bisect the east wall of the north-south hallway roughly 30' down." Huh? Sometimes a map is almost a necessity. Too much detail to form and hold an accurate picture of.
Third, the miniatures just look cool and help the person visualize each member of the party, their enemies, etc.
Fourth, you can take a break to go out for food or whatever, or even retire for the night, and there is no confusion about who was where.
In my experience, the game has only ever been improved using mats and minis. I remember once, many years ago, I got one of those giant vinyl models of a huge dragon - the wings were about 2' across. The party was going up against a great wyrm red dragon. I had them all close their eyes when they came across it, put it down on the table, and said something like: "Now open your eyes and you'll see what the source of that smoke and fire was..."
Their eyes popped out of their heads, a few people jumped out of their chairs, and they were 50 times more excited than they would have been had I simply described it to them. So yeah, I like it.
I guess when it boils down to it, I don't really use anything for my players (Rarely anyway). I simply make maps, keep them behind my DM screen and describe everything... every room, every hallway, everything. So they never need a visual aid besides me. Isn't that the DM's job in the first place guys?
I agree 100% - it absolutely is! I describe sights, smells, sounds, etc. Usually in exquisite detail - the color of stain and type of wood that the wizard's curio cabinet is made of. The smell of the incense in the cleric's temple and the sounds the chanting priests are making. The smell of the loam and flowers and the fresh scent of water near the river while running through the forest. And so on.
But as in the examples I gave, sometimes the info is too complex. Someone (one of the players) will inevitably have to see the layout of the area visually - which means drawing a map, because the description is so complex. And if we're going to draw a map, why not make it look good?
I'd argue that mats and minis only help to serve as a tool for a DM, not a crutch. I'd take a DM simply describing everything as you do over a DM who simply draws stuff without describing anything. But when you have a DM who describes things well and draws stuff to accompany or compliment those descriptions...oh yeah!