Dark Grey hex- Unsurveyed space. This is space that most military ships can enter (except the "War" classes). With years of effort, survey ships can turn it into an income producing system, or with a few months of work a scout can just incorporate it into the empire.
White hex- Surveyed space (also known as "Open Space"). Most empires have areas of space that have minimal interesting "stuff" in them.
Light Grey hex- Surveyed space with a trade route in it. This is a major convoy route in it. Think of this as a part of the USA's Interstate system. Some areas are flyover country, others have even more interesting things in them.
+ - A hex with a "+" in it contains a minor system. They produce some income and with further investment can be upgraded into...
O - A hex with an "O" in it has a major system. These systems produce much more income than a minor system.
* - If there is a base in the Open Space hex, it will be shown with this symbol. Exactly what type of base it is you'll have to get near enough to figure out.
Green hex- These are large radiation zones. They are not intense enough to be harmful to organic life, but they interfere with sensors, minefields, and cloaking devices.
dot on a hex spine- A hex spine with a dot in it represents a minefield.
Solid line on a hex spine- A hex spine with a solid line along it is a border.
Lines in the middle of a hex - This is a front line as two empires slug it out.
The two UnNav space areas show signs of surveying. The Lyrans are the current economic powerhouse with 15 major systems. The Romulans also have 15 systems, but haven't managed to bring them up to their full economic potential.
What could well be the opening shots in the "General War" is happening in ISC space. The ISC, Alunda, and FRAX are fighting in what was ISC space. The Drex and Gorn are involved to a lesser degree. Rumors of still more empires being active too are unconfirmed.