Does it mean you can't own anything and all your needs are provided for?
first, yes; second, no
I hope our resident Religious would chime in. I think they can answer this better. :)
Pardon me for my former, short reply.
The vow of poverty says, "I will own nothing". For our Franciscan teachers, that meant they did not own even the pen in their pocket. Any gift which they received was given to the Prior, who could allow them to use the gift (pen, wristwatch) with the knowledge and understanding that the gift was the property of the community.
Yes, all their needs were provided for by the community. This is the truest meaning of communism, as was described for the early Church in Acts. The community received income from various sources: Mass stipends for the priests, retreats held by members of the community, gifts, bequests, and other chaplaincy services that might be supplied for the surrounding community. At our school, the Franciscan Brothers operated a farm to provide food, and a wood shop to build furniture (mostly for the community).
If you, on your own (highly unusual), take a vow of poverty, you must trust G-d to supply your needs. Such was done by the desert fathers and monks, and I would guess they were supplied according to their faith in the LORD's providence.....which is very similar to the faith expressed by Catholics who truly tithe.
Hope this is a bit better (I know it's longer) explanation.