Who has copyright?
‘Copyright protection subsists from the time the work is created in fixed form. The copyright in the work of authorship immediately becomes the property of the author who created the work. Only the author or those deriving their rights through the author can rightfully claim copyright.’
(International / US Law definition)

In plain words: the person who wrote the work has the full copyright.
e-LyricZ is no copyright registering body.
You have and keep the copyright because you wrote the work.

What does it mean that I keep full copyright?
By submitting your work on e-LyricZ you do not wave your rights.
You keep full ownership of your work. You only give e-LyricZ permission to show it on the website..

How can I be sure no one steals my writings?
If you publish you never can be sure.
As soon as you go public (on the web, in magazines etc) with your work there is a risk that someone will use your work without your permission or even using it pretending they wrote it.
So the only way to be sure no one steals your work is to keep it in a draw at home and have no one ever read it.
But that hardly looks like a real option.

Where can I get more extensive information on copyright?
US Copyright (Library of Congress)
Internet Copyright Information Center