Combat is a large part of this game and has many things to know. The town maps are squares and combat is hexagons and reminiscent of old strategy games.
Units stats basics:
Attack: Damage done
Defence: reduces damage taken
Speed: both iniviative and movement rate
Range: range in hexes you can attack
HP: All units at every age have 10 Hit Points
Retaliation: If a melee survives an attack it will counter attack the unit next to it.
At the bottom of the screen is the order units act in. This order does not change and just cycles. It is important to know what unit goes next as you may be able to kill it before it acts after your unit.
When targeting a unit it will show the range of damage that will be done to the defender and how much the defender can do if it qualifies for retaliation. If the minimum damage is more than the total life of the defender it will say retaliation 0-0 damage since it is dead. If the attacker is a ranged unit it will still say a retaliation damage even if the target is not in melee range.
Terrain: All units except fast units have some sort of terrain advantage. Ranged units and artillery units do bonus damage on theirs and light units and heavy units have better defence on theirs.
Stats in depth:
Attack/Defence: Damage done is not linear. A spearfighter (light unit class) has 7 attack and 7 defence. You would expect it to do 0 damage. Base damage is 4-6 +/- attackers attack - defenders defence. It is not linear thought. The spearfighter would do 4-6 damage. If they attack a slinger (ranged unit class) who has defence of 3 that is their 6 Att - 3 Def = 3. You might expect it to do 3 extra damge but not so. It seems to be at least for bronze every 3 points over the defence = +1 damage done expressed as 5-7 instead of 4-6. The spearfighter would do 5-7 damage. That means the average damage done for it would be 6. A slightly above average attack but it will survive it at full HP.
Defence: Having less defence is not as terrible as it sounds since the damage is not 1:1. having a few points less Def is not the end of the world for the unit.
Speed: The units on each side with the most speed act first. If attacker and defender have a unit with the same speed the attackers goes first. Speed is not how far you move 1:1. Plain is 2 move. For exact terrains and units speeds go to http://forgeofempires.wikia.com/wiki/Movement_Cost
Range: Ranged and artillery units generally get more range as the ages advance. Range is a defensive feature because it allows you to attack while staying out of their range. Later ranged classes get enough range to shot over slow terrains and they cant move up to attack them through slow terrains.
HP: never changes. To heal hp you can pay crystals, delete the unit and build an other or let it regenerate over time. Every unit in the building that makes it says how long to heal 1 bar of life when out of combat. HP also effects the attack strength of units. When a unit takes damage it does less damage. A unit at 1 bar of life still does damage but is reduced even more to the point of almost being no damage. It is like changing your damage from ranged units to artillery units with very low hp.
Retaliation: If a ranged class stands next to a melee class and attacks the melee class can counter attack. The the attacking and defending unit are the same and both start with the same life the attackers will do say 4-6 damage and the retaliating unit since it took damage will do less damage and do say 3-5 damage. The damage is still significant but gives the advantage to the attacker. The damage predicted to do and receive are based on what terrains they are both on. If the attacker is a light unit and is on plains but plans to attack from trees it will not show the range of damage correctly until in forests.
A unit can only retaliate 1 time between its individual turns. This makes if possible for light units to kill heavy units by swarming it and only getting retaliated 1 time.
Terrain: Fast unit and artillery unit cant move on rocks. Artillery unit cant move on swamps. Not normally an issue but can be at times. Proper use of terrains can make or break the combat. It is often worth 1 extra turn to get on the terrain you need rather than charge in and attack the enemy.