Conformance checking is a sub-discipline of process mining, which compares observed process traces with a process model to analyze whether the process execution conforms with or deviates from the process design. Organizations can leverage this analysis, for example to check whether their processes comply with internal or external regulations or to identify potential improvements. Gaining these insights requires suitable visualizations, which make complex results accessible and actionable. So far, however, the development of conformance checking visualizations has largely been left to tool vendors. As a result, current tools offer a wide variety of visual representations for conformance checking, but the analytical purposes they serve often remain unclear. However, without a systematic understanding of these purposes, it is difficult to evaluate the visualizations' usefulness. Such an evaluation hence requires a deeper understanding of conformance checking as an analysis domain. To this end, we propose a task taxonomy, which categorizes the tasks that can occur when conducting conformance checking analyses. This taxonomy supports researchers in determining the purpose of visualizations, specifying relevant conformance checking tasks in terms of their goal, means, constraint type, data characteristics, data target, and data cardinality. Combining concepts from process mining and visual analytics, we address researchers from both disciplines to enable and support closer collaborations.