Universally Unique IDs (or UUIDs, for short) are a series of strings generated by one of a number of algorithms, that are guaranteed (in a practical sense) to be unique once generated, universally.
The practical limitation of the uniqueness of these strings is such that duplicates are not 100% probable until every person on the planet generated about 600 million UUIDs. As we do not compare every UUID ever made against every other (your program's UUIDs are probably never compared with another program's, for example), you are more or less guaranteed by statistics, that your UUIDs are always unique. Regardless of what machine they are generated on, or how many you generate.
The benefit of this is simple: You can tag stuff globally, persist the ID between world restarts and share these IDs among many servers, and each ID will still be unique, without having to do any fancy recording or checking, or any central savefile, website or database.