Break and brake, pronounced the same, have many meanings, as both verbs and nouns.
To break means to divide, to separate, or to damage. A break is a gap, space, or division. Break has many different uses:
We will break the bread into pieces so everyone can have some.
Everybody needs a break from work to recharge.
There was a prison-break last night; three men broke out (escaped).
In fact, the word breakfast comes from break-fast, where a fast is a period of not eating. The popular slang Gimme a break! Means “I think that you are being so ridiculous that I am begging you to give me a break (a rest) from your ridiculousness.”
To brake means “to use brakes.” With the word brake, the noun defines the verb—a brake is part of a car (or any machine, possibly). The brakes are parts that cause cars to slow down and stop—if you step on the brake-pedal. There can be other kinds of brakes, but the word mainly refers to land-vehicles.
Since brakes slow you down, to brake also means “(to cause) to slow down”; when we use brake this way, we often say put the brakes on:
If he doesn’t put the brakes on his eating, he will die young.
You are talking too fast; please put the brakes on!
The noun brake has some other meanings that are not used much anymore. An interesting one that you might hear is “an area of wetland (swamp or marsh) overgrown with plants.”