New to D2. Can someone explain item tiers to me?

I'm at around 410~ light now after having done a few expansions, and starting to think about gear for raids and dungeons.

I know that weapons of higher tiers have more perks to choose from, but that's kinda it. I'm unsure about armour, and wondering if tiers matter for a weapon with a natural godroll? Do they affect anything else? And are there consistent ways to only get high tier equipment?

Thanks in advance from a confused new player.