The thing that makes it so easy is that it operates on fax. It seems antiquated, but that means any restaurant with a phone line can offer all the modern conveniences without even having a computer on-site. Small business owners are super busy and constantly being pitched to buy services they don't have time to set up, but this takes no setup -- sign this contract giving us $x for any new orders we send your way, tell us your delivery radius, put a fax machine in your store, and you're now online. GrubHub can do the hard work of putting their menu online and running the website.
When a new order comes in, the restaurant gets a fax (and fax machines confirm receipt, so GrubHub knows it got there). You, as the customer, now get online ordering, re-ordering of previous orders with just a few clicks or taps, prepay with a credit card (or not), etc.