These words are homonyms (i.e., they are pronounced the same) but have very different meanings.
Leek is a noun, the name for a plant very similar to a green onion in both appearance and flavor; the image below shows what leeks look like:
Leak can be a verb or noun; it describes the situation when liquid comes through a small opening, such as a crack, in a container or barrier—including not only small objects like cups, shoes, etc., but also parts of houses, vehicles, and even human bodies. The word can be used in several ways; these sentences have the same meaning, as shown in the following sentence examples:
Leak as a verb:
Intransitive verb (no object): The roof leaks.
Intransitive verb with preposition: Water leaks in through the roof.
Transitive verb (with object): The roof is leaking water.
Leak as a noun:
There is a leak in the roof.
Leak also has two common metaphorical usages—the first is for a person releasing information that was supposed to be secret:
Edward Snowden is still in trouble for leaking our government’s secrets.
The second metaphorical usage of leak is not very polite (and a little funny):
After I drank too much water, I had to take a leak.
The above expression is only used casually, among friends, or in other very informal situations—but definitely do not use this expression in formal or polite settings!