Thalaiva is nothing but the same as Thalaivar, which in Tamil means a leader, boss, and is spoken for Rajinikanth with respect, like 'sir'.
The word comes from 'Thala' which means head, and means the one who heads people, hence leader.
The word is shown in Chennai Express' Lungi Dance song which is supposedly a dedication to Rajnikanth Ji.
For the Translation of Entire Lungi Dance, check THIS POST.
For all Lyrics, Translations, Meanings and Reviews from Chennai Express, go HERE.