Clauses have two distinguishing features: (a) they are enclosed by [square brackets]; (b) they contain a PREDICATOR.
There are two basic types of clauses: MAIN CLAUSE (MCl) and SUBORDINATE CLAUSE (SCl). If a sentence contains only one clause, ie. it is a SIMPLE sentence, that clause will be a main clause. Sentence 3 below is a COMPOUND sentence consisting of two main clauses linked by the co-ordinating conjunction and. There is ellipsis of the subject (he) in the second clause.
Sentences 4 and 5 below are COMPLEX sentences, each containing a main clause and a subordinate clause (subclause). The brackets of the subclause come within those of the main clause to indicate the dependent status of the subclause.
The Adverbial Clause (ACl) in sentence (5) is an example of DIRECT SUBORDINATION, ie. of a clause subordinated within another clause: [ [ ] ].
The NCl in sentence (4) is also an example of direct subordination. Another term for subordination is EMBEDDING, which suggests how one element is included in another.