Barkskin specifies that your AC can’t be lower than 16 while you are affected by the spell. This means you effectively ignore any modifiers to your AC-including your Dexterity modifier, your armor, a shield, and cover-unless your AC is higher than 16. For example, if your AC is normally 14, it’s 16 while barkskin is on you. If your AC is normally 15 and you have half cover, your AC is 17; barkskin isn’t relevant in this case.