Basically, units in Advance Wars 2 are divided into three groups: Ground units, Naval units and Air units.
Ground
Infantry
The Infantry unit is the basic Ground unit, and is the cheapest, with a base cost of 1000. It is the weakest of all units offensively, and it's main strengths lie in its ability to capture buildings and to act as "meat shields".
Mech
The Mech unit is a step up from the Infantry; it costs 3000 and is slower than the Infantry, only being able to move two squares in open terrain, but packs a rocket launcher that is used against vehicles to great effect. Like the Infantry, it can also capture buildings.
Recon
The Recon unit is the cheapest vehicle available, but is both very fast - especially on roads - and can kill Infantry or Mech units easily. Also, when playing on maps with Fog of War activated, they have a greater line of sight than most other units.
APC
The APC unit is the troop carrier of the game - it cannot attack, as it has no weapons, but can transport one unit of either Infantry or Mech, supply any units it is next to and also soak up a lot of fire before being destroyed.
Tank
The Tank is the first anti-armour vehicle - it can move over a relatively long distance thanks to its tracks and is useful against both infantry, with the machine guns, and light vehicles such as Recons or enemy Tanks with their cannons.