A Complex Sentence has one main clause and one or more Subordinate Clauses.The main clause or Principal clause makes complete sense by itself and does not need other clause for its complete meaning. It is, thus, of an independent nature. But the Subordinate clauses depend on the principal clause for their meaning. For instance, in
    The President said | that he believed in women education
      (Principal clause)                          (Subordinate clause)
The principal clause makes complete sense by itself but the subordinate clause does not.
Co-ordinate clauses are those which are complete sentences in themselves,that is,they have a subject and a finite verb of their own, but are a part of a large sentence joined by the co-ordinate conjunction. For instance,in
    The path was well lighted and we could see our way.
both the parts contain a subject and a predicate of their own ie, Principal or Main clause. Each par is, therefore,a sentence which is part of a large sentence. In other words, each part is a clause joined by a co-ordinate conjunction and, So it is a Co-ordinate clause.
Thus, a clause is a group of  words which forms part of a larger sentence and has a subject and a verb.
2. Clauses - kinds
    Clauses are of the three kinds :
         (a) Principal or main clause
         (b) Subordinate or Dependent clause
         (c) Co-ordinate clause
3. Subordinate clauses - kinds
   Subordinate or Dependent clauses are of four kinds. There are:
(a)The Noun clause which does the work of a Noun.
           All know that he is a qualified doctor.
that he is a qualified doctor is the subject of the verb know and also does the work of an object of this verb also. Here it does the work of a noun. So it is a Noun clause.
(b) The Adjective Clause which does the work of an adjective.
          This is the boy who met us yesterday on the road.
who met us yesterday on the road tells us about the boy and it, therefore,does the work of an adjective.It is, therefore, an Adjectival clause.
(c)The Adverb clause which does the work of an Adverb.
       I met my old student when i went to the bank.
when I went to the bank qualifies the verb and it does the work of an Adverb here. It is, therefore, an Adverbial clause.
(d)The Non-finite clause contains a participle or an infinitive (a non-finite) but no finite verb.
             My mother went to market to buy fruits.
to buys fruits is a non-finite verb.So this clause is called a Non-finite clause.