Learn Spanish (Latin America): El hombre del bigote es mi tío.

In English, we describe someone's physical features by saying they are "the man with the mustache." In Spanish, it is very common to use de (of) for this kind of identifying description. So, el hombre del bigote literally means "the man of the mustache."

What exactly is the word del?

It is a mandatory contraction. Whenever the preposition de (of/from) is followed directly by the masculine word for "the", which is el, they must combine into the single word del.

Why do we use es here and not está?

We use es (from the verb ser) because we are talking about identity and family relationships. Stating who someone is (mi tío) is a defining fact about them, which always requires ser rather than estar.

Is the 'h' in hombre pronounced?

No, the letter 'h' is always completely silent in Spanish. You pronounce hombre as if it started with the 'o'.