Basically there are shifty companies out there who monitor and report filesharing activities to the ISPs and while they have no legal standing to disconnect you, they can presure the ISP to. Or in worst case contact the owner of whatever copyrighted material you were supposedly sharing and they in turn could bring a lawsuit. That's a lengthy process though and it usually stops at threatening letters/mails and if you're not in the US the system isn't as much based on throwing lawsuits left and right to make a quick buck.
Protect yourself by removing exactly the file(s) they specified in their blackmail letter(s) from your uploads. That satisfies their demands and they'd have to find another specific file to send another letter. Some ISPs will disconnect you for repeated infractions though, but most won't care.
The easiest protection is to aquire and set up a VPN (use google), or use programs like Peerblock and such. A non-transparent VPN is the best and most secure choice though. Worst case, switch ISP to one less easily swayed by threatening anti-p2p companies.
One of these anti-p2p companies is irdeto, you can read up on their policy here. Read a bit between the lines and you'll see what they can and can not do. (I don't wish to post a clickable link but simply copy & correct the hxxp to http). hxxp://irdeto.com/takedown-notice.html