Sometimes active users decide to retire from, or leave, Wikipedia. Users may choose to retire after specific unpleasant experiences, or simply due to a loss of interest. Semi-retiring means a user's activity levels significantly drop, while they don't leave Wikipedia entirely. Retirement should not be confused with wikibreaks; the former is generally a permanent status, rather than a temporary break. Users who have retired may return at any point, though multiple, temporary retirements are discouraged as unnecessary drama.
Retirement is just another way of saying that a user has permanently left Wikipedia. Users generally retire due to either a loss of interest in contributing to Wikipedia, out of necessity due to personal reasons, or a combination of those factors. Personal reasons for retiring may include starting a new job, going off to college or otherwise experiencing a life-changing event that will no longer allow the person to contribute in the foreseeable future. If a user expects their personal life to temporarily interfere with their Wikipedia activity, they may want to consider using one of the many wikibreak templates as opposed to a retirement one.
Complete loss of interest in Wikipedia, on the other hand, might come naturally, but it more often results from one or many negative experiences on Wikipedia. These experiences might be bitter disputes, harsh review at an RfA, being blocked or partially banned, being desysopped etc.
Regardless of the reason, declaring retirement (rather than silently leaving) can be seen as an "official" statement that a user does not intend to return; thus, unnecessary future attempts at communication can be averted.
Semi-retirement is similar to retirement, but it means that the user has become less active instead of completely inactive. What this means can vary widely; one semi-retired editor who previously made thousands of edits per month may only make a few hundred, while another semi-retired editor may only drop by to edit every couple of months. Regardless, the point is that communication with a semi-retired editor is still possible, though they may take a very long time to respond.