What does a 'triumph of mediocrity" mean?
They've watched spoiled childern grow up to become triumphs of mediocrity-feeble, whining creatures who are going to need their hands held all their lives- and they're not going to let that happen to their son.

What does 'triumphs of mediocrity" mean here?
And, why they are going to need their hands held all their lives?

Question

What does a 'triumph of mediocrity" mean?
They've watched spoiled childern grow up to become triumphs of mediocrity-feeble, whining creatures who are going to need their hands held all their lives- and they're not going to let that happen to their son.

What does 'triumphs of mediocrity" mean here? 
And, why they are going to need their hands held all their lives?

Answer

They are spoiled children and I guess you know that spoiled children are not really strong enough to start a life of independence so they always need their hands held. Triumph of mediocrity generally means an average triumph, not a very outstanding one. This kind of triumph is not counted as a triumph actually!