Experience separates old units from new units, and provides incremental increases to certain combat stats.

• Any non-mindless unit will gain 1xp each turn that they're alive.
• Entering appropriate sites (commander and troops under command) will give extra xp per turn, but the amount depends on site in question.
• Experience granting items give the appropriate amount each turn (on top of survival and being in certain sites), but NOT to Animals.
• Wishing for experience grants some amount I haven't determined (apparently 500).
• Winning the arena gives 100 xp.
• Adventure sites grant 20 xp per turn that you're in them.
• Mummification may add together the experience values of the two parts of the mummy bundle, I don't yet understand this properly.
• Attacking in melee grants 1 xp. Your melee kills are kept track of separately from your total kills, both of which can be seen by clicking on the stat.
• Each square that you Trample grants 1 xp. Squashing a unit underfoot counts as a melee kill, by the way.
• Events can alter experience.
• Certain shapechanging will remove xp when changing shape, such as mounts losing their riders.
• Units that retreated in battle gain 1 xp.
• Units that didn't retreat instead get 4 xp.