The "table is full" error in MySQL occurs when the database reaches its maximum capacity, causing frustration for users. This error can be caused by a disk reaching its limit, too many columns in a table, or large files taking up space on the disk. To resolve this issue, it's essential to check disk usage and ensure there's enough space available. The solution involves changing the max value for the key 'innodb_data_file_path' to a larger value and saving the config file, then restarting the MySQL database. Additionally, users can try auto-extending the size without specifying the maximum size or increase the size limit for MyISAM tables.