A puzzle cache is a particular type of unknown/mystery cache where the owner has not given the correct coordinates on the page, but instead, requires you to solve a problem before finding the cache. These problems can range from finding coordinates in an image to doing a math problem to solving an encryption.
Generally, puzzle caches follow two schemes of solving for coordinates. One is that the coordinates can be solved from the cache listing itself, without needing to be on-site to gather data. Sometimes this might require research into a particular field, such as looking up statistics or encoding tables.
The other scheme requires the cache hunter to visit a given location or set of locations in order to gather data required to solve the puzzle. Usually this differs from an offset cache in that a general area is given instead of a coordinate or set of coordinates. One good example would be walking along a designated trail and gathering information from along that trail.
Sometimes a hybrid of both schemes are used. Often this involves solving a puzzle beforehand, then going to the solved coordinates to gather data for a later stage.