A political compass is a 2-dimensional mapping of a set of political opinions. An individual's political views are usually represented as a dot on this 2D grid. It is more complex than the one-dimensional left-right spectrum, because it delineates two axes. On some mappings, there is an economic axes and social axes. More popular mappings delineate left-vs-right and authoritarian-vs-libertarian.
According to proponents, the usual left-vs-right spectrum is to simplistic because it cannot represent certain similarities and differences between people's views. For example, an authoritarian right-winger and authoritarian left-winger might have more in common with each other than two libertarian left and right wingers.
The political compass might still be considered reductionist. In particular, when someone falls in the middle of an axis, it is not clear what set of positions got them there. For example, two people can both be listed as economic centrists if they take the right wing position on half of economic issues, despite the fact that they take opposite positions from one another and disagree on every issue.
In addition, when someone is placed in the center of an axis, it is not apparent whether they are moderate on each relevant issue, or whether they have strong opinions on all of the issues but align with each side half of the time.
Neither of the previous criticisms are specific to the political compass. A more hotly debated criticism is whether the political compass accurately represents the topology of the political landscape. One alternative proposal is the trichotomy, among others.