Levels matter because you can only learn Skills, Techs and start Tests depending on your level, the main wiki pages provide the details you need as to what you can do when, and what you have to do to acquire a skill or start a test. Skills are learnt from Schools and a tuiton fee is required from each player to learn any given skill. Techs are learnt from Universities and are free as other players have paid the research costs.
There are seven disciplines in Egypt and each has its own Initiate (Init) test. These are designed to give you an idea of what you can expect from each discipline and passing them gives you a level. You do not have to do all the Init tests before starting on "real" Tests, but you do have to be the required level.
The Disciplines are
Signing up for any test will give you a tab on the left hand side of the screen which shows you what you have to do to gain a level from that test.
For "real" tests, you gain a level from completing the principles, as this tab is known, but not necessarily from completing a test itself. "Real" tests are hard to pass and some can take many months to do so, Principles are usually much easier to achieve. This should not stop you trying to pass tests. They are a key achievements in Egypt and many give extra benefits, such as Body tests giving permanent improvement to your stats.
The exception to not getting a level for passing a test is that you do get a level when your title changes for your highest discipline. Titles depend on the number of tests passed in a single discpline.