"I had the students read the article". is a complex clause because it is made from two clauses. 

(I had (the students read the article)).

"the students read the article" is a complete clause on its own. It has a subject (the students),  a predicate (read), and object (the article). It is called an embedded clause because it is inside the clause "I had ...". The verb "had" this these sentence needs a clause as its complement. The structure is something like this:

Subj:   I

Verb:  had

Complement:

    Subj: The students

    Verb: read

    Obj: the article.

Long story short It is called embedded because it appears inside another clause. Note that a sentence is basically just a clause from the perspective of linguistics. A clause is a group of words that have a subject and predicate.

I hope that helps,

Fletcher