Security rating of a system controls a lot of stuff.

First off EVE only shows you the first number of the security rating, not the full value, which can run from 1.0 to -1.0. Anything less 0 is shown as 0.

High sec or Empire 1.0 No rats, Veldspar, Scordite, player sec status of -2.0 or better, no anchoring
0.9 No rats, more minerals (depending on sovernty), player sec status of -2.5 or better, no anchoring
0.8 Some rats, better minerals, player sec status of -3.0 or better, POS anchoring with charters and very high standing
0.7 More rats, better minerals, player sec status of -3.5 or better, POS anchoring with charters and standing
0.6 Cruiser Rats possible, better minerals, player sec status of -4.0 or better, POS anchoring with charters and standing
0.5 Cruiser Rats possible, better minerals, player sec status of -4.5 or better, POS anchoring with charters and standing

1.0 to 0.5 Police Forces and sentry guns shoot the criminally flagged

Low Sec:
0.4 Cruiser Rats possible, better minerals, no restrictions on player sec statsus, POS anchoring with charters and standing
0.3-0.1 BC rats possible, better minerals no restrictions on player sec, can build Starbases

0.4 to 0.1 Sentry Guns shoot the criminally flagged. The police won't show up, making low sec pirating possible (and low sec very dangerous. Probably the most dangerous space.)

0.0 to -1.0: all systems displayed as 0.0, no security hits for attacking other players, pirate battleships can spawn, no police or CONCORD response to player actions, most value resources and highest bounty ships.

Minerals get weird because they are controlled by sovereignty too, this table shows it nicely: http://www.eve-wiki.net/index.php?title=Ore

http://www.eve-wiki.net/index.php?title=System_security