As long as it is equipped to the chest equipment slot, anyone can wear a set of armor and benefit from it. The point of armor is to replace your normal default armor class with a higher number so it’s more difficult for an attacker to damage you head on.

If you are proficient with an armor, you can benefit from a higher armor class and benefit from the armor passive listed on the armor.

However, not being proficient with an armor means that when you put on the armor, while you will still benefit from a higher armor class, you will have disadvantage on all physical rolls, your speed is halved, and you cannot benefit from the armor passive listed on the armor.

Anyone can use a shield, you don’t need proficiency with it