Once you have installed the agent and configured MySQL monitoring, you will start seeing stats about your MySQL server.
This article is for the v1 agent and will eventually be removed. See v2 agent MySQL guide for replication monitoring with the v2 agent
The important metric is "seconds behind master" because as this shows how far behind the master the slave is. As this increases, the slave is getting increasingly behind.
You should create alerts for this metric so you can be notified when it starts getting too far behind. A good baseline value is 300 or 600 seconds i.e. 5 or 10 minutes. This allows for some variation e.g. networking issues but doesn't let it get too far behind.
Monitoring MySQL replication failure and errors
If MySQL replication fails completely then the agent will return -1 for "seconds behind master". You should create a separate alert for this value so you can be notified when there is a failure.
Note this requires version 1.13.2 of the monitoring agent.