Monk Tashi was one of five monks in charge of the Southern Air Temple. This elder was one of the monks who told Aang of his Avatar status, and was very strict and adamant about getting the young Air Nomad to train.
When the Council of Elders grew concerned about imminent war, he and the other council members decided to tell Aang of his destiny as the Avatar at the premature age of twelve. When the young Avatar doubted his destiny, Tashi showed him the Avatar relics. Upon witnessing his childhood toys, Aang stated that he just chose them because they seemed fun, contradicting Monk Tashi's statement that he had chosen them subconsciously among thousands of toys because they were familiar to his previous lives.
Much to his dismay, Tashi later discovered that Aang and his guardian, Monk Gyatso, were playing a game of Pai Sho instead of training. Believing that the Avatar should be training instead of playing games, he beckoned Aang to follow him to be tested on some high level airbending techniques. Agitated when Gyatso countered him, this incident caused Tashi to complain to Monk Pasang about Aang and Gyatso's relationship. Although Gyatso argued that Aang needed to grow up as a normal boy, Pasang sided with Tashi and decided it was best for the world if Aang and Gyatso were separated. To that end, Aang was to be sent to the Eastern Air Temple to complete his training.
A short time later, Tashi was killed along with the other Air Nomads during the Air Nomad Genocide.