Apple Watch

Simplified: A cellular model connect via your iPhone carrier (for a monthly fee, of course), allowing the watch to operate independently from the paired iPhone. The non cellular needs the phone to access the internet and cellular signal(i.e., you need the phone close by).

A cellular enabled Apple Watch will let you stream music, use maps and iMessages etc. while the watch is being used away from your phone. A non-cellular watch needs your phone close by in order to do the same. Be aware that the extra cellular data connection usually costs extra per month and does not just tie into your existing data package.