If you look in the top right of your screen you'll see information about the system you're currently in -
Nearest: Tells you what celestial body you're closest to in the system, planets are designated by roman numerals and moons are designated by plain old arabic numbers. So for example the trade hub of the galaxy is the Caldari Navy Assembly Plant in orbit around Jita IV - Moon 4. Similarly asteroid belts orbit planets so you might be mining in 'Altrinur X - Asteroid Belt 3'. A few planets in the game have names hand picked, these don't follow the regular naming convention. Some special celestial beacons will have names that appear here too.
Name: System names generally come from CCP's random system name generator with a few special cases that are added by hand - Jita, Rens, Hek are random names. Amarr, Luminaire, Old Man Star are from the game designers. Once you get into 0.0 space the names turn into random alphanumeric strings like 'HED-GP', 'D-GTMI' & '49-U6U'. All systems in wormhole space are named starting with the letter J, followed by 6 digits - e.g. J145452
Constellation: Constellation names refer to a small group of systems, the naming conventions are the same as systems with most appearing to be randomly generated. Constellations don't really matter too much right now, but in the pre-Dominion days it was important to player alliances to control whole constellations for better sovreignty claims.
Region: Regions on the most part have human readable names, even in the deepest drone regions where machine intelligence rules the names are poetic like 'Cobalt Edge' and 'Outer Passage'. Regions are hugely important to game mechanics, markets are split along regions and you can only see buy/sell offers in the region you're in. Each region generally has one NPC faction in control and one Pirate faction appearing in asteroid belts and exploration sites.
Security Level: Every system has a security level from -1.0 to 1.0, however this level is only displayed if it's >0.0, but if you look in the database dumps you can find the true security status. Higher security levels generally mean safer systems for law abiding citizens, and more threats for pirates, or enemies of the authorities who control the region.