To extend on what other people have said. Your ships Frame Shift Drive Module generally controls how far you can jump in a single jump. That, combined with the size of your fuel tank (also upgradeable) will define how easy it will be for you to get around. Combine a decent graded set of those with a fuel scoop and the galaxy is yours.
Those 'lines' on the map aren't universal, they are what
your ship has calculated as jump capable routes based on your ship's current set up. Bigger ships, or exploration centric ships (asp, adder e.t.c.) will have a higher jump range and larger fuel storage capacity as standard compared to other ships of the same size.
The galaxy map travel lines will update and change based on what your ship currently has installed in respect to travel based mosdules (FSD, over all weight/mass, amount in cargo hold (extra mass), Fuel capacity, current fuel stored, and so on).
You can also change the routes calculated from 'economical' to 'fastest' in the galaxy map. This will recalculate them, giving you more direct routes outward, at the expense of a shorter distance applicable to your fuel capacity within the 100LY radius. Of course this is capped by the absolute range of your FSD and bound by the mass of your ship compared to that.
Try stripping all modules off your sidewinder and installing an A class FSD, then go look at those lines