To disclaim is to deny, usually in order to avoid blame. If you push your brother and he trips and falls, you might disclaim responsibility for the action, saying he is just clumsy.
If you decide to go skydiving, the company you dive with will likely you ask you to sign a disclaimer of liability. This is a form that says you will not sue the company if you injure yourself on the dive. In it, they disclaim liability for your undertaking this dangerous activity. Obligations to do something and product warranties can also be disclaimed which means that they will not be honored.