In version 5.6 MySQL introduced a feature called fulltext indices. LiveAgent application utilizes the fulltext indexes to speed up searching in contacts (if you don't use Elasticsearch), but it is also used in filtering tickets by tags and filtering contacts by contact groups.
If you install LiveAgent on database MySQL 5.6 or higher, the columns are already created with fulltext indices and you don't need to do anything. However, if you installed LiveAgent on database version MySQL 5.5 or older, the tables and columns were created without fulltext indices and you will have to add the indices manually. An error saying "SQLSTATE[HY000]: General error: 1191 Can't find FULLTEXT index matching the column list SQL" might appear in the logs.
LiveAgent source files contain the SQL commands to add the indices. You will find them in /install/db/gpf/innodbfulltext.sql , /install/db/la/innodbfulltext.sql and /install/db/la/innodbfulltextdownloadable.sql. The scripts add fulltext index to all the columns that require it. You just have to execute the SQL script on your LiveAgent database.