A URL is the address of some resource on the web, which means that normally you type the address into a browser and you get something back. There are other type of resources than web pages, but that's the easiest conceptually. The browser goes out somewhere on the internet and accesses something.
A URI is just a unique string that uniquely identifies something, commonly a namespace. Sometimes they look like a URL that you could type into the address bar of your web browser, but it doesn't have to point to any physical resource on the web.
URI is the more generic term, and a URL is a particular type of URI in that a URL has to uniquely identify some resource on the web.