It sounds like you're experiencing packet loss. Two things that you can do to determine what is the cause of this, assuming you're using Windows:
Open up Command Prompt. Type in ping 192.168.1.1 -t
It will start pinging your router. Let it run for one or two minutes, take note of how long it takes to ping your router or if the request times out.
Open up another window of Command Prompt. Type in ping google.com -t
Do the same thing.
If requests are timing out when you ping your router, your router may need to be updated. This means that the packet loss is directly the cause of your router. If requests time out when you ping google.com but not when you ping your router, it is purely your Internet Service Provider and you need to call them about your service.
Another few things that you can do to make sure there's no trouble:
Make sure your cables are all plugged in and snug. If you can use a shorter cable, that's even better as it takes less time to travel between your router, modem, and your computer. Power cycle your router and modem. This means turn off your router first, and then your modem. Leave them both off for two minutes, and then turn your modem back on. Let it boot up before powering on your router. Connect everything and do the same test again. Usually, this helps. Just do it every so often to keep your connectio
EDIT:
I realize I didn't explain what packet loss is. Packet loss is the term for when information (i.e. you clicking on the map of League of Legends) is sent but not received. You can still receive information, which is why you still see everything moving around you. You could even lose your connection if the packet loss is significant enough. I also really want to stress the need for good communication with your ISP. They can help more than I.