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.