There are basically four types of logs
1) The Error Log
The error log contains information indicating when mysqld was started and stopped and also any critical errors that occur while the server is running.
2) General Query Log
The general query log is a general record of what mysqld is doing. The server writes information to this log when clients connect or disconnect, and it logs each SQL statement received from clients.
3) Binary Log
The binary log contains “events” that describe database changes such as table creation operations or changes to table data. It also contains events for statements that potentially could have made changes
4) Slow Query Log
The slow query log consists of SQL statements that took more than long_query_time seconds to execute. The minimum and default values of long_query_time are 1 and 10, respectively.
All other files you can read easily but to read Binary log you have to use a MySQL utility program called mysqlbinlog