A good starting place for SNMP information can be found here.
SNMP traps are messages which are originated by some device or application and are sent to a management system (i.e. a monitoring system).
For example, a network switch could generate a trap when some port goes down and send it to a monitoring solution which will generate some kind of alert to notify people about the failure. A UPS could generate a trap when the battery levels are too low or when the load is too high. They could also generate a trap to notify that a previous event has been cleared.
Traps are asynchronous messages. The management system does not request them.
OTOH, a monitoring system could use SNMP to request performance or other type of measures to the monitored devices and they would respond to those requests if they are properly configured. These would also be SNMP messages but they are synchornous and thus, they are not SNMP traps.