Response system is technology in each yoyo that makes friction between body of a yoyo and a string. Thanks to the response system modern yoyos can wind up and also spin when you throw them.
There is several kinds of response systems (pads, starburst, o-rings, etc.) but 95% of yoyos nowadays use thin pads (19mm). You can always check which response system is which yoyo using by checking the details page at each product page.
Response systems needs to be changed once you feel the yoyo is not getting enough spin when you are throwing it or when the yoyo is having trouble reacting to your Binds. For example 19mm thin pads need to be changed every 1-3 months. Changing them is quite easy, just use sharp tool to get them out, clean the pad seat from old glue and just stick in new pad. Make sure it sits perfectly in its place, you do not want any part of it being loose or reaching out in the gap of your yoyo as it would significantly decrease yoyo's performance.