Questions: Quel, quels, quelle, quelles = Which / what ?

You already know that Que or Qu'est-ce que at the start of a question is used to ask what something is (See Qu'est-ce que c'est... and Qu'est-ce que c'est que ça/cela ? = What is... / What's that?,  C'est quoi, Qu'est-ce que c'est ? = What's that?).

Now look at these questions:

Quel est ton film préféré?
Which / What is your favourite movie?

Quels bonbons tu as choisis?
Which/What sweets did you choose?

Quelle jupe tu veux?
Which/What skirt do you want?

Quelles chaussures te plaisent?
Which shoes do you like?

Quelle est la plus belle princesse du royaume ?
Who is the prettiest princess in the kingdom?

Quel garçon a jeté cette balle ?
Which boy threw that ball?

Note that the question adjective quel also means "What/Who?" (and "Which?") in French.

So when to use quel  instead of que/quoi/qui ? 

Whereas que/quoi/qui will be used to define something, to ask what they are, quel is used in the context of a choice, an alternative: what is that, relative to other elements?

Note also that Quel is an adjective, so it always relates to a noun (thing/person). Therefore, it will be used when the question "What/Who" is really "What/Which <thing/person>...?" or "What is <thing>" or "Who is <person>?":

Quelle est votre adresse ?
What is your address?

  ->  Here the adjective quelle goes with adresse (What address?)

 

Quel acteur voudrais-tu rencontrer ?
Which actor would you like to meet?

  ->  Here the adjective quel goes with acteur (Which actor?)

 

Quel parfum de glace tu préfères ?
Which ice cream flavour do you prefer?

->  Here the adjective quel goes with parfum (Which flavour?)

 

Quelle est la personne que tu admires le plus ?
Who is the person you admire the most?

  ->  Here the adjective quelle goes with personne (Which person?)

 

ATTENTION: 
Quel is an adjective, so it agrees in number and gender with the thing/person it is used with ("quel", "quels", "quelle", or "quelles").

 
Case of lequel, laquelle, lesquels, lesquelles

These are pronouns, which means they're replacing pre-mentioned nouns (i.e. "Which one(s) ...?).
Therefore, they'll be used when the thing they refer to has already been mentioned, to emphasise the question:

Mets tes chaussures !
- Lesquelles ?
Put your shoes on!
- Which ones?

J'adore les bonbons !
- Oui, mais lesquels sont tes préférés ?
I love sweets!
- Yes, but which ones are your favourite?

Note that the noun is not mentioned in the question, as lequel, laquelle... already expresses it: it would be redundant!

 

See also Quel, quelle, quels, quelles + noun = What a ...