I keep hearing people talking about high sec and low sec space, and others talk about 1.0, 0.5 and 0.0. What does it all mean?
1.0-0.5 high-sec space. If anyone attacks you there they will be flagged as a criminal, and killed by Concord (If a player with criminal flag doesn't lose his ship while in hi-sec it's considered an exploit). Note that Concord reaction time may vary and if the attacker is able to deliver enough damage before Concord arrives you will die.
0.4-0.1 low-sec space. There is no Concord in low-sec space and you are much more likely to be attacked by other pilots in low-sec. The attacker gets criminally flagged and if there are any sentry guns nearby he will be shot at by those guns. Sentry guns are present at gates and stations only. There are no sentry guns at asteroid belts, planets or moons.
0.0 null-sec space. There are no laws. Caution: there are some systems that show up as 0.0 but actually aren't null-sec space. If a system shows up as 0.0 but there are sentry guns at gates it's low-sec space with true security status slightly above 0.0 (for example Hophib in Aridia).
True security status is a number between -1.0 and 1.0. The game interface shows all systems with true SS below 0 as 0.0. For systems with positive security status only one digit after the decimal point is visible.
In systems with lower true security status you are more likely to find rats with higher bounty and better types of ore to mine.
To find out true security status of a system go to: http://eve.grismar.net/ssec/index.php
Basically it's the amount of security CONCORD (the police) provides. In 1.0-0.5 there's still CONCORD around. In 1.0 they'll respond the quickest. In 0.4-0.1 there's no police, but your security standing will go down if you attack someone (PvP). 0.0 (null-sec) is the PvP zone where actual fights are done. Stay away from there if you're not experienced, and in general if you don't know the area and aren't in a group.