There was apparently some A/B testing of this some days ago, see Anna Lear's comment here:
We're currently A/B testing this feature [next badge/privilege progress in the achievements drop-down] to see how it performs. ... No promises on whether we'd add an option to disable it (assuming we decide to keep it), but I will say that if we see overall positive results in user behaviour, we'll put more time into making the next badge/privilege tracker more usable in the dropdown.
If you are no longer seeing it, I guess the testing is over, and SE will decide what to do with this. (Note that some users saw this while working on some computers, but not while working on others.)
