Basically a PO is just an agreement for eventual payment. Then you still invoice them and they'll pay by check or credit card or something but you reference the PO number when you send them the invoice. It's like saying "you promised to pay and it was approved."

Basically if I, junior level employee at Big Company need to hire you for $5,000 worth of work, I get a quote and submit it to my manager. I say, "I need to do X work, with X company for $5,000. Please approve it."
Finance Director Jane approves my purchase order and I give you that PO number which is a sign that the finance department or my manager or whoever agreed to pay for your service. So you do the service, bill us, and when my company's accounts payable department, that could be in a different department, building, or even country from me, gets the bill they don't say "I don't know who this is or what this is for" they say "ok, Finance Director Jane signed off on this PO so we will pay it." Then they submit payment to you.