fermer à clef means to lock something. You can also use fermer à clé with exactly the same meaning, since clé and clef are synonymous. It’s worth noting that even though these both literally mean “close by key”, there does not have to be a key envolved in the locking process, for example you could use fermer à clé when referring to a toilet cubicle door, which doesn’t use a key. (It may be useful if some natives confirm this, but I’m pretty sure this is the case)

Another verb for to lock would be verrouiller, but fermer à clé is probably more common in everyday language.

In answer to your other question, you would translate that phrase as

I will therefore lock my door…. (to be certain that nobody can get into my house)

à est associé à fermer, et non à porte. Cela signifie avec dans ce cas.

• fermer à clef : avec une clef

• fermer à double tour : avec / en faisant un double tour

• fermer à fond : jusqu’au fond

• fermer à mort (forme familière) : jusqu’à la mort (jusqu’au bout, au maximum)