Dungeons & Dragons is best described as a "tabletop roleplaying game" but is by no means restricted to the tops of tables. In the years that I've been playing D&D I have seen a whole spectrum of approaches to the game; from low fidelity where it's little more than an interactive campfire story, to high fidelity where everyone has custom 3D printed figures on hand-painted scenery. For the most part it comes down to the people you play with that make the game (I'm talking like 95% here). Some of the best missions I've run have been mapped out using rulers, shredded paper and foreign currency. But being a westerner, I am a sucker for nice things.
During postgraduate study I may or may not have had unsupervised access to 3D printers and laser cutters. Now I want to be clear; I was entirely responsible in my (ab)use of university resources. I bought my own materials and only used the machinery when everyone else was done for the day. When asked by the technician what I was cutting a grid for, I calmly and honestly explained that "it's for a game. I'm a game designer." The fact that those two points were mutually exclusive was never brought up...
...so I have these now...
D&D is a game of communication. The DM communicates a narrative. The players communicate their actions. The DM communicates the resulting consequences. The players communicate their regret. It's a constant back and forth. You could play sessions without rolling a single dice if it's set up that way. A good DM can weave an enthralling story, completely capturing the players' imaginations and good players can lose themselves in their characters and the world, using their crafted persona to help the world come alive.
The other half of the game, however, can be very technical. There are a lot of rules that help action flow in a manageable stream that prevents things from degrading to people yelling at one another. Having a physical representation of everything on the table eases this further. It provides an anchor for the game where the players can physically see where everything is relative to everything else. Such a 'map' enables them to visualise, plan and react to the going-ons of the game without getting lost in confusing descriptions. But there's something more going on here than just points on a grid.
The addition of physical miniatures adds a visual and tactile element that players can interact with. A custom figurine that represents one's character is a great way of reinforcing the personal connection players innately have them. It's your unique character. They're a real thing. I mean, look at them. They're right there.
Likewise, when they encounter foes on their quests, physical tokens create impact. "10 zombies" sounds about as threatening as "16 zombies" when you read or hear it because they're both numbers the mean 'lots'. But when there's sixteen zombie tokens in front of you, filling the room and tripping over one another for a chance to chew your cheeks, your one little character looks mighty lonesome by comparison. I've often found describing an encounter and simply placing the horde on-board can be the difference between players responding with "oh yeah" and "oh god."
Similarly, larger tokens generate a sense of immensity. Regardless of what the tokens represent, they're intimidating because they tower over your character. On the table they may be no more than ten centimetres tall but by comparison to the heroes, they can appear monstrous. It's the same difference between hearing and seeing 'many,' and hearing and seeing 'massive.' Admittedly there's also something satisfying as a DM about slamming a huge counter on the table for some added drama.
Most of the pieces I have I found on thingiverse and scaled them to match a ratio of 4cm:5ft. I went for a number of simple items that can be representative of various things; barrels, crates, pillars, chairs etc., spray painting them black to make them as unobtrusive as possible. Their purpose is to help give the environment shape, not to distract players. I've seen custom miniatures for specific environments and enemies where each piece has an incredible amount of detail. Believe me, these high quality tokens are amazing for immersion. It's why so many people repurpose Warhammer miniatures and environments for D&D campaigns. The one problem is they aren't quite as versatile. Like a good ghost story, the more you leave to the imagination, the more people can engage with it. And don't be surprised that the PCs don't trust the barkeep when he's represented by a six-inch tall Tyranid mind-spanker.
On that note, I chose to keep my enemy tokens super simple. I found the low-poly skull on thingiverse and took it into Maya to add the base and numbering. The choice of skull was simply to give the impression of danger but apart from that, I kept them generic to act as vessels for whatever threat they are supposed to be. Much like my black feature tokens, these are meant to shape the encounter while the players' imagination colours it.
Of course the printed tokens and laser cut tiles are ideal for my current style of play, but I only recently had access to the resources that allowed me to make such a kit. I used to accomplish all this with a bag of foreign currency. Papa Brebner managed by converting an old backgammon set into a D&D treasure trove, numbering the tiles and borrowing props from my medieval Lego castle set. Our main game board was a cardboard chess board from which he devised the scale for all the miniatures he drew. It was low-fi gear with high-fi effort put into it but to me and my sister it was the toolbox from which we built countless adventures.
D&D is a game of imagination so a DM's kit can be made from pretty much anything. Whether your converting a chessboard, building everything from Lego, using cardboard propped up on bulldog clips, sculpt models from clay or a mix of everything, it all works. As I said at the start; 95% of the joy of the game comes from the people you play it with. But having a good kit is cool too. If no-one in your crew has any artistic skill and wants to draw up some miniatures for you, you can always look into sites like HeroForge to generate some for the PCs. It feels pretty special to have a unique miniature for your D&D brain baby.