"Please eat vegetables."
In this case the verb in the てform acts as 'please eat', you tell the other person what action you want them to do.
In japanese vebs changes not only by time tenses but by 'nuance' also.
食べたい(です) -want to eat. 食べよう/食べましょう-let's eat.
The てform also connects verbs, and this stemp can be used for other grammers like:
食べて(い)る/食べています - am/is/are eating.