Pursuit, in simple words, is to chase or follow. In Kabaddi, it comes into play when defenders chase the raider, who after entering the baulk line and touching his defenders, tries to return his court.
Pursuit is permissible when a raider is on the run back to his court, after either successful or otherwise raid. On the other hand, it is not permissible when the raider delays his chant, attempts double raid, scrambling after struggle.