DISCLAIMER: These are rough guidelines based on my (Megan's) experience with Southern California Collegiate competitions. You should ALWAYS check the rules for each particular competition--such as those for the UCR Orange Blossom Ball and the Caltech Dance of the Roses.

Another good resource is Ballroom 101 on the USA Dance website:
http://www.usabda.org/usabda/pdf/ballroom_101.pdf

Summary

Syllabus levels: These consist of levels at which you are restricted to a certain set of dance figures (closed syllabus). Complete syllabi can be found at:
http://www.usistd.org/index.php?option=com_content&task=view&id=39&Itemid=51

While any event can be designated closed or open syllabus, at most Southern California collegiate competitions the closed syllabus levels are:

Newcomer: The only level at which participation is strictly limited (which is good-this means beginners won't be competing against those with lots of competitive experience!). Generally, you must have been dancing for less than a year and have little or no competitive experience. Figures are generally restricted to bronze syllabus.

Bronze: For those with somewhat more dance experience. At most competitions, each competitor is allowed to dance in two adjacent syllabus levels--so beginners can, for instance, enter both the newcomer and bronze categories (and even if you don't win, it's fun and the extra experience is always good!).

Above those levels are silver and gold, which dancers proceed to as they master the lower levels.

Multi-dance events: These events are generally entered by silver+ level dancers. The levels are typically pre-novice, novice, pre-championship, and championship. While these events can be designated closed or open syllabus, they are usually (at collegiate competitions) open, meaning there are no choreography restrictions.

Even if you're not at the level to begin competing in these categories, they are very entertaining/inspiring to watch (in addition, of course, to the professional showcase), so be sure to stick around and enjoy all the amazing dancing, costumes, and choreography!

Nightclub events: There are just one or two levels for the nightclub dances at most collegiate competitions (Salsa, Argentine Tango, Lindy, etc.): beginner and intermediate/advanced. It is up to each dancer to decide which level he/she feels is appropriate.

Determining your level: At many competitions it is against the rules to dance at a level that you have "placed out of." Many competitions use the YCN proficiency points system:
http://ballroomatmaryland.com/competitions/ppoints_rules.php
in which you earn points for placing 1st-3rd at a given level. Once you earn a certain number of points, you must move to the next level in that dance.
Note: the Orange Blossom Ball does not use any such points system.