Employment Offer Acceptance Letter I Was Just Recently Hired And The Acceptance Letter Stated "contingent Upon Successful Completion "?

I was just recently hired and the acceptance letter stated "contingent upon successful completion "? - employment offer acceptance letter

What this means, the acceptance letter at the end of a floor and declared that the offer "employment at will". The question is: "Is the employer going to do background checks and other pre-recruitment after departure, or that the employer has already done background checks on rent me and others before. I ask myself, because I have some problems with the background to have, and I told the HR representative when I called and asked if he could come to an interview I did not know who would be employed on the site. I wish I knew what he was able to or expect the Company will go back and explain that has verfications and do not meet the criteria, please. Help!