Extrapolating From the UWP
Perhaps one of the most useful skills a Traveller Referee can possess is the ability to extrapolate and improvise on the UWP, or Universal World Profile, which is discussed fully on page 171 of the Mongoose Traveller Core Rulebook.
This string of digits is used to hold a large amount of information about a planet. It allows Referees to create data on planets quickly, so that a ref can be ready to respond to that wild hair that the players have, when they say they want to go here, rather than there.
It's not necessary to generate an entire universe, first of all. You only need generate those planets which the players can travel to in one jump, assuming you are using the standard Jump Drive of Traveller. Since the highest Jump Rating is 6, many refs use a J-6 map, which plots all the hexes surrounding the planet the players are currently on. Most beginning player ships have only Jump-1 or Jump-2, so you could even restrict yourself to a range of one or two hexes, but putting together a J-6 map is a good idea anyway, since you never know when players are going to steal that J-5 yacht. Ahem. It also allows to to get a good feel for the 'neighborhood', as many planets will be aware (depending on their Tech level) of the planets in the surrounding six parsecs to a greater detail than planets farther away.
Even if you are using a commercially available background with its own system maps, putting together a J-6 map allows you to think in more detail about the planets in the surrounding area.
Once you have done this, look at the codes you have generated or looked up in a sourcebook. Write down, in plain English, what each of the codes mean. Then you can begin to see how the planet fits together.
For example, consider a planet with a mid-range tech levels, with a population in the billions, which is not balkanized, and is a religious dictatorship with mid-range law levels. That means there is one government, based on a religious system which oversees an entire planet, that has been around long enough to develop a large population since the initial colonization of the planet. They don't possess sufficient technology to monitor the citizens all the time (hence the mid-range tech level). That probably means that power isn't as centralized as the government would like, and perhaps implies that various mid-range religious officials (bishops?) hold a great deal of power in the their respective dioceses, though ultimate power is vested in the religious leader. The population indicates that the planet was colonized long ago, perhaps as a band of pilgrims that were fleeing religious persecution elsewhere.
As you can see, the bare bones of the UWP can be fleshed out considerably, and if you do a little of this work before you hit the table, you will be better prepared when the players go, "OK, once we have stolen the yacht, we sell off all the gold fixtures to improve the Jump engines to J-4, and then travel to Annwyn, which is one of those planets mentioned on Verana's old star maps..."