Proficiency is the ability for a character to use something sufficiently. Proficiency with armor and weapons is granted by your Class, and sometimes by your Race.

Weapon and Armor Proficiency

Using a weapon without Proficiency:

If you attack with a weapon you are not proficient with, any attacks made with the weapon are made at disadvantage.

Using armor without Proficiency:

If you are wearing armor you are not proficient with, you have disadvantage on any ability check, saving throw, or attack roll that involves Strength or Dexterity, and you can't cast spells.