EXPLORING:

You're in a "Sector".  There are 54 sectors in an 8x8 grid (not all the positions are used), numbered 0,0 thru 7,7.  Each sector has up to four "gates" to adjacent sectors in the far North, South, East,
and West of the sector.  Gates look like huge rings - you fly through them to enter the next sector (remember the training exercise?).  Most sectors are missing one or more of the four possible gates.  The sector you're in, Seizewell, has no East gate.
Seizewell is controlled by the Teladi, who control several other sectors as well.  As you explore, you'll encounter five other races; the Borons, the Argons, the Paranids, the Split, and the dreaded Xenons.  They're not automatically your friends.
There are maps available on several websites; it's also a lot of fun to make your own.  It's a big world out there - you'll need lots of scratch paper.
(Tip) Stay in Seizewell until you have the Tac Nav system - it's too hard to figure out directions without it.
(Tip) It's almost impossible to get the name of the sector correctly from the garbled sound as you enter it.  Look on the (P)ilot screen, the log at the bottom gives the name of each sector you enter.