When you have electronics such as ESC/motors on the same power curcut that you use with other sensitive electronics such as FPV cameras and transmitters they can cause slight spikes in the voltage.
A view of the voltage with an oscilloscope, the right image shows the voltage spikes have been halved by adding a filter into the circuit
Normally this does not cause any noticeable problems as most R/C equipment such as your R/C receiver is able to handle this with this build in circuitry. However the most obvious effect of this is on your FPV equipment by showing up as lines on your camera. This is because most cameras where not exactly designed to be mounted onto R/C aircraft.
An LC filter is a basic circuit that forces the electricity to pass through an Inductor (denoted by L) and Capacitor (denoted by C) to form an electrical resonator. In effect the Inductor filters out high frequency noise, and the Capacitor filters out low frequency noise, resulting in a nice clean line of electricity.
Since the motors/ESC are the biggest cause of noise, depending ont eh size of motors/ESC you use you might not need an LC filter with your FPV gear. In some extreme cases an LC filter will not be able to properly filter out the noise, in which case you should use a separate battery to power your FPV gear.
Lastly here is a great detailed video that talks about this in much more detail and also shows you how to build your own power filter (where I got the oscilloscope images from).
Hope that helps