Porte means door, qui means who and claque means slap.
How does this mean Slamming door?
I am not able to understand the usage of qui here?
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When you say for instance "Il y a une porte qui claque au premier étage." you mean that on the first floor a door is more or less regularly but constantly being banged against its door jamb by a draught. You use the same construction for other things, in particular windows and shutters, that are subjected to this action of the wind or of draughts.
There is an important matter of context which makes the difference between the meaning given to the verb in what precedes and a meaning very similar. That meaning of the verb is "to bang against something once or to close with a bang". It might be difficult to make out which is which.
The OP is asking about the usage of qui, qui is a relative pronoun (un pronom relatif) that replaces the word preceding it (l'antécédent) and usually acts as a subject. The sentence after qui is a subordonnée relative complément de l'antécédent meaning it complements that word. An English analogy would be who, this is the guy who loves you, who is replacing the guy here in the same way that qui replaced the door.