In order for a male non-Jew to become Jewish he needs to do three things which all must be performed in front of a Beis Din (panel of 3 judges.) Those are that he must have a bris milah, accept upon himself the Mitzvos and go to the mikveh. For a woman it's the same thing (less the bris milah of course.)
However what would be the din of a person that (let's say in a woman's case where there is no bris involved) accepted upon herself the mitzvas and then went into a kosher mikveh without a Beis Din present. Or perhaps there were only 1 or 2 Jewish people present. Or perhaps there were three present but not all were "orthodox" Jews.
It seems that while one should definitely have a Beis Din lichatchila, would would be the din b'dieved (post facto) if they didn't have an "official" beis din?