Ordinal logistic regression is a type of logistic regression (link) that deals with dependent variables that are ordinal – that is, there are multiple response levels and they have a specific order,  but no exact spacing between the levels.  For example, you might be interested in correlating political views (measured as very conservative, conservative, moderate, liberal, very liberal) with demographic and other variables.

By far the most commonly used ordinal regression technique is the proportional odds method, but there are others, and there are times when ordinal data should be analyzed using multinomial logistic regression or linear regression.  This is so, in part, because the differences between nominal, ordinal, interval and ratio level data are not exact – many variables do not fit neatly into one category.