When. On arriving somewhere and stopping there — stepping down at a rest halt, into a hotel room, onto a campsite, at a house where you will sleep. It belongs to the moment of alighting, and its scope is the place, not the journey. A traveller who moves five times in a day says it five times.
The words. Kalimat Allah at-tammat, the perfect words of Allah. Tamm is completeness in the sense of nothing missing — the root of tamam, a thing finished, with no gap left for anything to enter. Refuge is being sought in speech that cannot fall short, which is the whole reason the adjective is there: a word that might not hold is no shelter.
What is being feared. Min sharri ma khalaq — from the evil of what He created. Not "from evil creation." Evil is placed in what created things do, and even that stays inside the created order. So the sentence, at the moment it names a danger, has already said the danger is on the near side of Allah's dominion, made and held like everything else. Nothing is granted independent power in the act of asking protection from it.
Why a place, specifically. A stranger's ground is unknown twice over: you cannot see what is in it, and you do not know its habits. The supplication does not ask for the place to be surveyed. It puts the unseen part of it under something that does not need to survey it.
Common confusion. A near-identical supplication uses the singular at-tammah and then names devils, vermin and the envious eye. That one is for protecting children and against the evil eye. This shorter one is the traveller's.