It grants you a one time boost to your max jump range, level 1 is 25%, level 2 is 50% and level 3 is 100%, so if you are stuck and cant get to that system 40Ly away, this is what the FSD boost is for.
You need to collect materials from planetary landings, and craft them into FSD Boost magic pellets. There are three levels of effectiveness depending on which materials combination you use.
Once you have FSD Boost magic pellets, you can use them to plot and execute long jumps as Whiterose described.