Update 2016-03-24: Removed dead VideoJug link.
A personal statement is a short paragraph about yourself near the top of a CV / résumé, which quickly gives the reader the most important information about you, and makes them interesting in hiring you for the job.
It can also be called a:
A similar idea is an objective statement (or objective), where you say what you want to achieve in the job you're applying for, but most advice nowadays say that objective statements are no longer useful. You can read about both profiles and objectives here.
Here are some links to useful articles about writing a personal statement on your CV / résumé.
G.A.L.E.S.L. / joe3
Some tips and links on learning English.