The word that here acts as a subordinating conjunction. It refers to the subordinate clause each time:
The use of biometric indicia for identification purposes requires...
This is your main clause (however, you could also see the entire sentence including the subordinate clauses as the main clause).
The following three sentences are your subordinate clauses, linked to require by that:
- that a particular biometric factor be unique for each individual
- that it be readily measured
- that it be invariant over time.
The three subordinate clauses are linked together through coordinated conjunctions (the comma and and) on their level.
Some additional information:
Your sentence is what we call a complex-compound sentence. A sentence with a main and a dependent clause is a complex sentence. One with two or more independent clauses is a compound sentence. In this case, your sentence is a complex sentence, but because it contains two or more dependent clauses that are coordinated (thus compound), your sentence is compound complex. If you turn this around and have multiple main clauses that have subclauses (dependent clauses), you get a compound-complex sentence.