Weight Training or Resistance training is when you perform movements that allow you to build muscle. You can do a google search for it and you should get a good introduction. You don't need weights you can do push ups and squats and similar movements.
Your own mother isn't supporting your efforts to improve your health?! That's insane. But I think it's fantastic that you have all that equipment so readily available! Just hop on one of the machines while you're watching TV.