With BT you can join BTFON which allows you to use other people's wireless connections.
I must be a bit thick but why would you want to share other peoples wireless connections? Surely that could be a security risk? (Unless you're meaning starbucks or other such business/social places and not private house connections)
If you are out and about it can be useful to connect to the internet to check something, browse the news, etc. You can do this at many wifi 'hotspots'. Anyone can use such hotspots in pubs, cafes, libraries etc.
BT run a system whereby you agree to allow others to use spare capacity on your connection via your wifi. If you agree to this you are then enabled to access any other similar BT customer's connection that happens to be in range. I must emphasise that BT customers can opt out - but they can't use other peoples and not allow others to use theirs.
This means that there are many, many thousands of hotspots available to BT customers instead of the few thousand available to everyone - if you are visiting someone who doesn't have wifi the odds are that a near neighbour will have a BT connection you can share. Or you are staying with friends who have a BT connection but would prefer not to give you their router access codes so you can use their connection. Or you are in a hotel that wants you to pay for wifi access - use a BT connection instead.
Security is supposedly not an issue - at least, no more than using any public hotspot.
Supposedly (I have no way of telling otherwise) the external user on your wifi would take a backseat when you are using the connection yourself - your traffic would have priority so you should, in theory, see no loss of performance.
In reality the system is perhaps most useful to smartphone users who can connect to the BT system for browsing via wifi rather than using up the data quota on their phone connection.
