This is a phrase that is common only in northern parts of Germany, maybe also in middle parts, but it is not used in the southern parts of the region where German is spoken. You won't hear it in Austria (this is where I live). And I guess that this phrase is also not very common in Bavaria. (I bet there will soon be comments that will help you narrow down the regional spread of this term.)
The main kinds of residing are
- in a whole house (mainly in rural regions, but also in suburbs of larger cities)
- in an apartment (mainly in urban regions)
Houses are almost always owned by the people who live in them. Either they built the house themselves or they bought it. So they are the owners. It is also possible to rent a house, but this is rare.
Apartments, on the other hand, are often not owned but rented. I only have figures from Austria, and there about 42% of all apartments are rented. This figure is slowly rising, while the proportion of owner-occupied apartments is getting smaller every year. I guess the situation in Germany and Switzerland is similar.
When you want to say that you live in an apartment that is rented, you usually say:
Ich wohne in einer Mietwohnung.
I live in a rented apartment.
Ich habe meine Wohnung gemietet.
I have rented my apartment.
These sentences can be said everywhere where German is spoken. But in northern regions also this phrase is in use, which is colloquial speech and means exactly the same:
Ich wohne zur Miete.
The verbatim English translation is "I live for rent" but when you say that in English, it sounds as strange as the German phrase sounds to me, because I live in a region where that phrase is not used. I even think that »Ich wohne zur Miete« is grammatically incorrect, but for sure there will be people with other opinions.