Instead of trying to explain the gory details of which bytes go where and when, we're going to start by describing the kinds of information you can get from a device that supports SNMP.
Generally, an SNMP device has a bunch of counters and string values inside that you can access using the SNMP protocol. For example, you might want to know how long a particular device has been up and running. Almost all SNMP-enabled devices have a counter indicating how long they have been up and by reading its value you can tell when it was last rebooted. If you monitor it on a regular basis, you can tell if the device has been rebooted because the counter goes back to zero when it is restarted.
Most SNMP-enabled devices have a very large number of counters available. For example, a switch with 32 ports will have multiple counters for each port that indicate each port's name, its status, its bandwidth usage, and more. Many devices will keep counters indicating how many processes are running on them including which ones are using how much CPU and memory they are using. Many network printers use SNMP to tell you all about their status including whether they are out of paper or not.
All of this information and more is available through SNMP and it provides a bounty of information that can and often should be monitored.