An "SNMP ping" is a method of achieving "heartbeat" or "keep-alive" functionality with SNMP communications.
A typical ICMP Ping is an IP-based signal sent from one device to another. If the target device receives the "ping" from the source device, it will (if configured to do so) respond to confirm that it is active and connected to the network. It's a nice, simple way of confirming that a device is online.
The problem with ICMP pings is that they operate on a fairly superficial layer. If you've worked with IP networks for a while, you've surely run across a situation where a device is "frozen" but can still respond to pings. In cases like this, a simple ping just isn't complex enough to be a good test of actual device status.
SNMP devices in your network support a more reliable ping method based on GET requests. As you'll recall, an SNMP GET message is sent by the manager to a device to request a specific value. If you want to know the temperature reading at a remote site right now, your manager will send a GET request to the local SNMP RTU to demand the sensor value.
SMART SNMP Managers
A smart SNMP manager can take advantage of the call-and-response GET mechanic to send a kind of "SNMP ping". On a automated schedule (one every 3 minutes, for example), your manager will send an SNMP GET to the device. If the device responds, all is well. If no response is received after a few successive requests, your manager can conclude that the device is offline and an alarm must be reported.
If you had only been using common ICMP pinging, your device might have continued to respond despite being in a failed state. Your monitoring system would have been vulnerable and you wouldn't have known it. SNMP-based pings, in this case, were a much better option to ensure your SNMP-based equipment was still online.