Hey! First off, GRATZ! Traveller Noob on finding the Best Sci-Fi Game Ever (tm).
Tech assumptions:
First off, understand that when Traveller was developed, Compaq was a serious competitor in the desktop market. Some of the first Traveller boards required a subscription to GEnie and CompuServe.

So, Traveller's tech grew with the times, and with Sci-Fi in general.
Here are the basics.
*Interstellar travel is possible, cheap, and almost (!) always safe. It has been a fact of life in this part of the galaxy for thousands of years. It is an on-ship engine does not require 'jump-gates', 'warp-tunnels', wormholes, etc. to work. It's called, btw, Jump Drive. Further, there is a set number of hours that a jump will take you (roughly 6-7 ship-days), and the higher power a drive have onboard dictates how far you'll go in that time. The range is 1 to 6 parcecs. As a note, the extra-dimensional space that jump drive carries you into is still not well understood.
*Interstellar communication is not possible. The news travels as fast as the ships do. This leaves corporate, military, planetary and independant personnel with wide lattitude to do their jobs.
*Fusion power is cheap, plentiful, and efficient. The standard fuel is hydrogen that can be scooped from gas giants, ice caps, or oceans and 'cracked' to remove excess oxygen.
*Computers are ubiquitous, but they are not uniform. There are several differing computers at various tech levels.
*Psionics is a real, recognised ability, if not fully understood. The ability, for example, is not hereditary and geneticists have not identified a 'psi-gene'. How a society deals with psi abilities plays a large role in politics.
*The universe teems with life, and the humanoid/bipedal form is very common. HOWever, each alien culture is a culture, not a human in a furry suit.
Beyond, this, everyone else seems to have covered alot.
Welcome to the board and to my favorite game ever.
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