Armor items have a base armor rating (based on the type of armor, eg Steel) that cannot be changed - but you can improve the effective armor rating (i.e. the number that appears on the item when you have it equipped) in a few ways:
Increasing the level of the armor skill relating to that type of armor (eg increased Heavy Armor skill will improve the rating you receive from heavy armor)
Unlocking armor perks in the respective skill tree (the first perk in the tree, i.e. Juggernaut for Heavy Armor or Agile Defender for Light Armor)
Unlocking the unison perk in the respective skill tree (Well Fitted for heavy armor, Custom Fit for light armor) and wearing four pieces of the same armor type to make it work
Improving the item via Smithing - the higher your Smithing skill, the better improved your armor will be, and having a Smithing perk associated to that armor type will also help
There's also a perk you can unlock through a quest which will give you a permanent +25% bonus if wearing Dwarven Armor.
Any of these methods will take effect immediately for armor you're already wearing - you won't need to create a new set to see the benefits, although you may need to unequip and re-equip your armor items before the benefits will be visible.
Bearing all of the above in mind, there is a hard cap of 80% physical damage reduction (567 in full armor without a shield, 542 in full armor with a shield, and 667 if unarmored), beyond which you'll see no additional benefits. The cap is easily reached before maxing out all of the above methods - so, for example, it's possible to achieve the armor cap with Steel armor if you've maxed out all other benefits; you don't necessarily need Dragon Armor to do it.
Source (UESP)