The rainbow term is something you may have come across when looking at guides here, or on the evony forum.
Put simply, the rainbow tactic involves sending a few troops of every type which are faster than your main army. This causes the enemy + their fortifications to attack the closer units, while your main army advances. This is a considerable advantage when using a archer army, done right it can allow the archers to fire at your enemy, without taking damage.
A decent rainbow tactic would look like this:
96,000 Archers
1000 Warriors
1000 Swordsmen
1000 Pikemen
1000 Cavalry
You may be wondering why i sent 1000 warriors, even though they are considerably slower than the archers. The reasons is that Archers, once in range, will stop and fire. This allows the warriors to overtake the archers and then draw fire, giving the archers another free round.
The rainbow tactic is a must when fighting experienced players, different rainbows are used for different purposes but most will look like the one shown.