SNMP stands for the Simple Network Management Protocol. At its heart, SNMP is a set of rules that allows a computer to get statistics from another computer across the Internet.
Computers keep track of various statistics that measure what they're doing. For example, routers can keep track of the number of bytes, packets, and errors that were transmitted and received on each interface (port). Web servers might keep a tally of the number of hits they have received. Other kinds of equipment has configuration information that's available through SNMP.