Crystal Oscillators will provide the necessary clock for the operation of microcontrollers.
Microcontrollers works on the basis of clock. Microcontrollers use common data bus for data transmission between different parts. Each peripherals and registers communicate each other by time division multiplexing. This is achieved though clock.
For example, to store data from a particular memory location to register A,
Clock 1 : Provides Location Address To Memory
Clock 2 : Provides Read Control Signal to Memory, which places data in the data bus
Clock 3 : Provides Clock to Register A, to store data available in the data bus.
This is only an example for understanding the working, actual process may differ for different microcontrollers.