A clause is basically a sentence that's inside of another sentence. Here's a sentence:
I love mushrooms.
And here is a sentence with a clause:
I told her that I love mushrooms.
Each clause has to have a subject ("I") and a verb ("love").
There are two kinds of clauses: dependent and independent. The example "I told her that I love mushrooms" is dependent. It's introduced by a word like "that", "which", "where", "how", "if", etc.
An independent clause is part of a sentence that's joined by "and", "but, "or", "however", or another conjunction. In this example, there are two independent clauses:
I love mushrooms and I eat them every day.