Armor is very important in the sense that it determines your damage reduction. Typing sc (score) is a quick way to see your current armor reduction. For example:
(171 H 105 M 0X): Arc the Scythe of Aramon (level 28)
171/195 Hit Points 105/112 Magic Points Armor: 616 (52%)
18518000 Experience 358,402 gold coins XP Needed: 0
By the way, that's terrible reduction for his level, but I've been lazy since I don't level him as much.
The higher the armor value, the higher the percentage goes, up to a max of 75% reduction (good luck getting that.) Some spells or skills can help raise this value, i.e. druid's barkskin and mage's armor spell.
Keep in mind there are also skills related to armor, the first is the defense skill, the next being the type of armor you can wear. These have a chance to raise on being hit, so for a class that stuns often like mage/lich, it may be harder to raise your Defense/Cloth skills. It's important to take some time to do this, otherwise you may lock yourself out of equipping higher level gear. When you look at an item you can see if it requires a certain skill amount (Requires at least Average in cloth). Other times the item may just have a level restriction that you won't find out until you are high enough to equip it. Raising the defense skill helps you to dodge hits completely (protection spell buffs defense +10), while raising armor skills allow for the equipping of higher level items that require higher skill.
While it makes the most sense to raise the best armor type equipable by your character, it doesn't hurt to work on other types of armor if you can. For example wearing one chain piece as a plate wearing character can help in the long run if you find chain gear that's better than your current plate. Another example is finding a cloth armor that comes imbued with resist magic, it may serve you better than a higher armor value plate item vs monsters that cast a lot.