1.0 - 0.5
Tends to be safe space. Small NPC rats that won't do too much damage. Everywhere (belts, gates, outside stations etc) are patrolled by CONCORD so if anyone attacks you (or if you attack anyone else) CONCORD will come along and make short work of your hard earned ship and all the lovely tech II components you've kitted it out with.
0.4 - 0.1
Low sec! You can be attacked in anywhere without CONCORD intervening! However, at gates and at stations the sentry guns will come into play and attack the attackers. There are no sentry gun at the belts!! NPC rats are medium sized and will cause a bit of damage if you ignore them.
0.0
Null Sec. You can be attacked anywhere. Nice big rats!
Depending on what your characters sec. status is will also decide what sec systems you can go in.
If your characters sec status is greater than -5.0 (e.g. -5.1, -5.2 etc) you are deemed and outlaw and can only stay in systems with a rating of 0.0 to 0.4. You can be attacked at gates without the sentries getting involved. However you can also attack back to defend yourself.
If your status is anything else negative e.g. -2.8 or -1.0 for example this will affect what hi sec systems you can enter. Can't remember the details but it's worth looking into if you aim to be naughty

.
Also important to note that if your at war with another corp/alliance, you can be attacked anywhere no matter what the sec status of the system your in.
No doubt I will have made a mistake or two so if anyone see's anything, point it out! Hope that helps.