Fibre is a means to connect your router to the internet.
Why is fibre better than ADSL or LTE?
Quite simply put, Fibre is up to 100 times faster than ADSL or LTE.
Think of it as a water pipe, ADSL is a very thin pipe, not much water (in this case data) can run through it.
LTE is like a spray, sometimes the water reaches you, and sometimes it doesn't, if you are far from an LTE tower, the signal will be bad and your speed will be either slow or unreliable.
With fibre, the pipe is big, and there is lots of water (data) that can go through it, at a reliable and fast speed.
The fibre goes to your router, and the router produces a wireless signal (wifi)
You can either connect your devices via a LAN cable, this ensures you always get the speed that the router receives.
With wifi, it is similar to the spray, it only reaches a certain distance, and when a wall is in the way the wifi signal will weaken, and you will not receive the full speed that the router produces. Typically routers reach a radius of 50meters in an open area.