Can someone please explain to me what a Purchase Order is ? Someone contacted me for a service and they said they "will be paying with Purchase Order". I do not want to sound like an idiot. But as someone who is providing the service, what specific action should I take when someone wants to pay with a Purchase Order ? Do I send an invoice ? We already agreed on the price, and I just wanted them to send me a check or pay online. This "purchase order" thing just threw me off. I do not know what to do next.

A purchase order is an offer to purchase goods and or services and it will list all terms of a sale including payment method. If you accept the purchase order from the other party, then there is a contract between both parties.

If the purchase order is unclear on the payment terms I would contact the other party and have them either modify the purchase order or have them send you a new one with a payment method that both of you will agree on.

Normally you would send an invoice when you bill the customer or when the material is shipped to the customer.

A purchase order is essentially a promise to pay. A company orders from you and PO details what that are ordering (or what service they will be getting) and the terms under which they are making the purchase (Price, shipping, tax, and payment terms). Many companies prefer to pay by PO because it provides a better paper trail for their records.

Before a company will accept payment by PO they will do a credit check of the company to determine whether they will pay. Also they will require the company to complete an application. Here's an example of such an application:
Business credit application - Templates - Office.com

If I were you, I would get back to them and tell them you are willing to accept a PO if they complete your credit app. And that the terms for the PO would be Net 10-30 days. You choose a time frame by which they need to make payment.

Thank you for the responses. So I as the service provider must now take the next step and send them a contract that they must agree to before I can provide the service ? There is no doubt that these people will pay so payment is not an issue here. Thanks.

If you accept the purchase order the contract has been formed because you accepted the conditions in the purchase order and because you are in agreement with the other party. So all you would need to do is fulfill the terms of the purchase order.

A PO IS a contract. So by them sending a PO, they are contracting with you for the service. You accept the PO by performing the service. Upon completion of the service, they then pay according to the terms of the PO.