This was going to be an intermediate level post, but this phrase is so popular that it's important for everyone to know how to use it. Right away! Pode deixar is one of those phrases that finds it's way into just about every conversation here.
Pode deixar: PODER (to be able to,can) + DEIXAR (to leave)
Easy Peasy Lemon Squeezy.
Pode deixar is the kissing cousin of deixa comigo.
I can do it.
Let me do it.
I'll take care of it.
I can handle it.
So, when you say pode deixar, what you're really saying is, você pode deixar para eu fazer.
No one will ever say all of that, but that's what it means.
You can say it straight up, or slightly sarcastic, or to convey confidence. It'a all about the delivery.
The last example is very advanced. He says:
» Tá. Assim que eu chegar em casa eu vou ler o documento.
» Pode deixar.
The "tá" is just "está bom" = Ok.
Brazilians say tá all_the_time. When said by itself it's always means Ok.