The concept of heavy infantry has been around for centuries, and generally described soldiers that were equipted with more armor and/or weaponry than the standard soldier. The hoplites of ancient Greece are good example of the early use heavy infantry. Later came heavy cavalry, which even later evolved into an extreme example of heavy infantry, the medieval knight; often so heavily armored and equipted they could not standup or mount their horse, without assistance from others.
 
When gunpowder hit the scene in the 14th century, the days of full body armor were on their way out. Light, Medium, and Heavy Infantry designations now basically referred only to how heavily armed the infantry was, and in modern times also correlates to the tasks they are expected to perform on the battlefield. Light infantry was highly mobile and lightly armed, and well suited for tactics such as infiltration. Heavy infantry was heavily armed and better in a defensive role.
 
In Axis and Allies RTS the heavy infantry regiment looks great on paper, with 3 MG's, a mortar, and a anti-tank infantry unit, no infantry has more raw firepower. So why don't we see it more often? Heavy infantry lacks sniper units, which means they usually get owned by commandos, SaS, and snipers. Also, it's available only to Great Britian, which has SaS, who matchup better versus enemy infantry due to their sniper units.
 

The primary benefit heavy infantry offer is the ability to put maximum firepower on target, dealing out AP, Explosive, and Morale damage.
 
Heavy infantry will not matchup well versus sniper-based infantry, so be sure to scout your enemies well, to avoid a matchup problem.
 
Heavy infantry works best when used in coordination with mech or armor, as they are often too weak to fight on their own, and too slow to finish off retreating vehicles.
 
Infantry is at a disadvantage versus mech and armor. Very important to keep your heavy infantry in benefitial terrain to help level the playing field.

There are two different types of formations, formation on the regiment level (Assault, Aggressive, and Column), and formations on the division level, which are a formation of a group of regiments.

Groups of regiments can also be put in the Assault, Aggressive, and Column formation by activating group behavior, but this is not recommended for combat, only for reorganizing your division if it becomes too spread out. That means most of the time your division should have custom formations with group behavior set to off. This also allows you to set the formation for each regiment in your division without affecting the group formation.

You will want to use different group formations for different game situations, some basic examples are seen on the left and right. The determining factors are usually what type of enemy regiments you are facing, and how many special op bombs your opponents have. Hotkeys are essential for effectively managing your divisions, so once you have selected and organized a group, save it by holding down [Ctrl] and pressing any of the keyboard number keys; or simply right click an spot on the group control bar.
 
Of course there are many other factors that influence a successful infantry campaign, see conclusion for more tips and links.

Get a basic idea of which upgrades effect which infantry units, and how to apply those upgrades in online play. Included is a suggested upgrade order to help newer players understand which upgrades are the most benefitial to their cause. See: Upgrading Your Infantry/Airborne