Q:

How should I understand "à" in "ma porte à clef"?

Le soir suivant, je voulus faire la même épreuve. Je fermai donc ma
  porte à clef pour être certain que personne ne pourrait pénétrer chez moi.
  Je m'endormis et je me réveillai comme chaque nuit. On avait bu toute
  l'eau que j'avais vue deux heures plus tôt.

In the second sentence of the excerpt above, what is the grammatical property of "à" there? My dictionary shows that it is a preposition. But there is no definite/indefinite article in front of "clef". Is "porte à clef" a phrase or something? 
My question concerns that how should I understand "Je fermai donc ma porte à clef" precisely in English. 

A:

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)

