A main clause is a clause capable of making a complete sentence by itself. A sentence always contains at least one main clause, and a simple sentence consists only of a single main clause.
In the simple sentence Alice started making dinner, the whole sentence is the main clause. In the compound sentence Peter cooked dinner, and Alice did the washing-up, there are two main clauses connected by and.
A clause which contains a subordinate clause within it.
In the complex sentence The employees who were dismissed are suing the company, the matrix clause is The employees … are suing the company, while the remainder who were dismissed is the subordinate clause contained within it.
A matrix clause is often a main clause, but it need not be: it can itself be a subordinate clause.