What is the role of time-base in CRO? What is the explanation of sawtooth voltage out put.?

Seems more a homework question...

The role of time-base is to synchronise the display of the CRO with the to be observed data signal.
The sawtooth signal of the time-base (horizontal) deflection signal builds up a picture that displays the to be observed data via the (vertical) deflection signal in a similar time and phase of that data, making it a stable and linear display.

:)