From Final Fantasy Wiki

Delay Attack and Delay Buster are special skills appearing in Final Fantasy X. They appear within Tidus' section of the Sphere Grid. With the inclusion of the Conditional Turn-Based battle system (CTB), the Delay skills, when successful, knock an enemy further down in the list of character turns. Unlike the Slow spell, Delay does not continually restrict the next turn of an enemy. Many enemy special attacks can also inflict a delay effect on the attacked party member.

The two skills reappeared in Final Fantasy X-2 as abilities for the Warrior Dressphere.