Contention is basically sharing. If you live in a house with teenage girls then you contend the bathroom with them - which can mean waiting hours to get in. Your electricity is contended - normally not a problem as there's more than enough to go around however tell that to the residents of California last year who had rolling blackouts due to a lack of generating capacity. Everything in life is contended - it's an effective way to utilise a shared resource.
Regarding ADSL - there are two levels of contention on the BTwholesale network at the moment:
If you take the worst case scenario for the home user then that means you're sharing your 500kbs with 49 other people. If you are all downloading at the same time then you'll get 10kbs - about a quarter of the speed of a normal dial-up analogue modem. In reality, it's unlikely BT will allow this to happen. Despite extremely rapid broadband takeup during 2003, most users are still able to download and upload at the maximum quoted speed.