According to Wikipedia, the term "analysis paralysis" or "paralysis of analysis" refers to over-analyzing (or over-thinking) a situation, so that a decision or action is never taken, in effect paralyzing the outcome. A decision can be treated as over-complicated, with too many detailed options, so that a choice is never made, rather than try something and change if a major problem arises. A person might be seeking the optimal or "perfect" solution upfront, and fear making any decision which could lead to erroneous results, when on the way to a better solution.
The phrase describes a situation where the opportunity cost of decision analysis exceeds the benefits that could be gained by enacting some decision, or an informal or non-deterministic situation where the sheer quantity of analysis overwhelms the decision-making process itself, thus preventing a decision. The phrase applies to any situation where analysis may be applied to help make a decision and may be a dysfunctional element of organizational behavior. This is often phrased as paralysis by analysis, in contrast to extinct by instinct (making a fatal decision based on hasty judgment or a gut-reaction).
BGG's Glossary defines analysis paralysis as such: when overanalysis and mini/maxing increase the downtime in a game beyond a desirable level. Sometimes abbreviated as ap in the forums.