It is when you own your flat, or more precisely, you become a member of a condo association and own a part of the property corresponding to your flat, as opposed to a "hyrd lägenhet" which is simply a hired flat which remains the property of the landlord.

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Note added at 25 mins (2008-10-27 09:29:22 GMT)
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consider "hyresrätt" vs "bostadsrätt"

The crucial difference between owning a house outright (freehold) and owning the leasehold (whether arrende or bostadsrätt) is surely that in the latter case you have only bought the right (rätt) to live there, not the bricks and mortar of which it is made. So your freedom to use or dispose of it is limited by the actual freeholder, who also has to agree to any future sale or transfer of the lease, in Sweden as in England. Plus you have to pay a monthly fee for general upkeep, fixed services etc. The special thing with a Swedish bostadsrätt is that the actual owner is a housing co-op which all leaseholders have to belong to, and not a private company. Housing co-ops in the UK can work like this but they also take other forms.
The relevant point in this translation however is presumably not who is the ultimate owner of the property but what value and/or level of financial commitment is involved, freehold being>leasehold>tenancy?
Incidentally a bostadsrätt in a villa as opposed to a block of flats is a new idea to me, is that common in other parts of Sweden perhaps?

Hej Ieva! Thanks for the clarification. As it's British English you could use a variant on 'Housing association' such as 'Housing association house'. It is not exactly the same kind of ownership as a bostadsrätt, but near enough to be a reasonable gauge of credit worthiness (which is what such kinds of question are often about).
'Tenant-owner (housing association)' might be an alternative if there's enough space.
All the best, Charlotte
Oh, and I've come across several 'bostadsrätt' housing estates here in Skåne; mostly semi-detached, but definitely houses not flats. And I'm pretty certain I've read about Stockholm and Kiruna ones in the old HSB glossy magazine.
[With apologies for any newby mistakes in format, formatting etc. etc.]

Better late than never.