Despite using miniatures in roleplaying games for years, it wasn't until I started playing wargames that I learned about miniature bases. And boy was I not prepared. A miniature base is the little plastic disc (or square or hexagon) that wargamers glue to the bottom of their models. To my great surprise, I quickly learned that the base has other functions aside from the practicality of making it so your miniature can stand up straight. It's a hugely significant part of a miniature, and is in fact the very foundation of the playing piece itself. Here's what you need to know about miniature bases, from pragmatic to poignant.
The base is the token
Mechanically, at least in theory, the base underneath your fancy looking miniature is the actual player token. If you proudly collect and love miniatures, this can be hard to accept, but the sum total of your meticulously crafted and painted model is the boring plastic disc underneath its feet. Deep down, we all know this to be true. Logically, we all understand that we could play a wargame using coins or chess pieces. We use miniatures because they're fun to paint, fun to look at, and fun to play with. But the game rules, with admittedly a few exceptions, are designed for bases. Foot soldiers are 25mm, commanders are 32mm, cavalry are 50mm or 60mm, and so on.
Base and physical size
The base also often determines visibility. Because miniature wargaming is a 3d game played with non-posable figurines, it can be confusing to decide whether an enemy model is behind cover or not. One common solution is to trace a straight line between the base of the attacker and the base of the defender. If anything blocks your path while tracing that line, then the target has at least partial cover. Why does this matter? Because should you be allowed to trace a line to any random part of the model, you're likely to be able to find some piece that's not behind cover. These models are not posable, after all, but we imagine that the models represent real people who can crouch down behind a boulder, lean against a wall, and generally make themselves a smaller target. Thanks to bases, however, we can all agree that a miniature can't make itself any smaller than its base size.
Base and movement speed
For example, the size of a base is why a miniature moves the distance it can move in a turn. There may be lore considerations, but you're not likely to see a 25mm base moving 10" each turn. Similarly, it's unlikely that a mech on a 100mm only moves 5" a turn (unless it's part of the model's lore that it's particularly slow moving). There are definitely exceptions, but the logic of how pieces move usually starts by considering the base size.
Base and miniature size
Related to targeting and cover, a base also usually defines what space a miniature can fit through. Our little plastic people can't move their limbs, so some of them are trapped for all time in an exciting and flamboyant pose. That looks pretty neat, but it some cases it can also mean a model can't literally fit through a doorway or a forest. You probably don't stretch your arms out laterally before walking through a doorway, so our soldiers in the game world would adjust to the height and width of their environment. But, as with the rules for cover, it's usually assumed that a miniature can't adjust to a size smaller than its base.
A base is a bounding box and represents reach
Not unrelated to the concept of physical size, a miniature's base often tells us something about its reach. Rules vary on this, but a miniature on a 25mm base probably can only engage in melee combat with another miniature that's within 25mm, and can only carry a ranged weapon with a certain range and power. A miniature on a 100mm base, on the other hand, is considerably larger, so it might carry a weapon that strikes at anything within 100mm. A big base like that often implies a greater toughness or resilience to attack, partly because an attacker can't get close enough to deal serious wounds.
When rules don't account directly for base size when determining weapon reach, they very often account for base size for judging when two miniatures are in physical contact. For the same reasons as cover rules and miniatures fitting through terrain features, it can be difficult to represent two non-posable plastic soldiers in physical contact.
It's not uncommon for a soldier to be posed as if running in for a charge, which is a lot different from a fighting stance. Also, many miniatures have lots of little tiny decorative parts that could get caught on the decorative parts of another miniature, so out of practicality it's useful for miniatures to not become literally entangled.
Instead, you can look at the bases of two miniatures. When two bases are touching, those miniatures are within reach of one another. When two bases are not touching, the miniatures are not within arm's reach.
A base defines formation
In a wargame that cares about formations (especially historical wargames), the way you base your miniatures can define your squad. This might have the mechanical purpose of ensuring no single squad is over-powered compared to your opponent, or it might determine how a squad can move, or whether your army or shield wall is broken. Whatever the purpose, the base may literally be the basis of how your army fights its battle.
A base suggests battlefield presence
Finally, on a purely emotional level, a miniature base suggests something about a miniature's charisma and battlefield presence. This is why you sometimes see a commanding officer on a 32mm base even though the model (and the person it represents in the game world) is physically the same size as a footsoldier on a 25mm base. Sometimes a big base for a commanding officer just represents the importance of the character. The commander's presence on the battlefield is significant, somehow, and the base size correlates to the symbolism the character has for its fellow troops.
Exceptions abound
Wargaming is a diverse hobby, so exceptions to these "rules" can be found in probably every game system. Sometimes, a base is just a stand for a miniature, and sometimes a base doesn't even exist. For tanks and other vehicles, for instance, a base might be redundant. However, the humble base is at the core of wargaming rules, regardless of whether it's explicitly cited. To a rules system, every token is some measurement out of the total area of the game board, and it rarely matters how you decorate it.
Read or re-read the rules for your game with an eye for how the bases of your miniatures interact with the rules. It might be illuminating, and hopefully I've avoided making any baseless claims (I promise this whole post wasn't written to justify that single pun).
Hattusian soldiers photo by Seth Kenlon. Creative Commons cc0.