What gets a paper rejected after conditional acceptance?
I have been a part of computer science program committees that actually do reject papers that do not meet the conditions of their acceptance.

In my experience, papers are generally classed into two categories, essentially corresponding to "minor revision" and "major revision" for a journal. The papers that are basically acceptable in their current state are in the first category, and the organizers mostly just trust that the camera-ready will be acceptable as well---after all, it's in the authors' interests to improve it further.  

Papers in the second category often get assigned a "shepherd" or, in rare cases, a second round of review, to ensure that they actually meet the minimum quality standards of a meeting. In my experience, this second category is much more rare than the first, and is not used by a large number of conferences.  In general:


The big first-tier conferences are often already overflowing with strong submissions, and don't need to bother about trying to cultivate borderline papers.
More specialized or not-quite-as-good conferences are more likely to make provisions to help turn borderline papers into solid papers, in order to make sure they end up with enough strong papers.
Low-ranked conferences often aren't very choosy in any case.


Turning to understanding the state of a particular paper: look at the process you've been told is going to happen. If you're being told about something like another round of evaluation or a shepherd, then your paper is likely borderline and you probably need to work hard to improve it to keep it from being rejected.  Otherwise, "conditional accept" is likely to be more a matter of wording than serious judgement questions.