Research in the explainability of optimisation techniques has largely focused on metaheuristics and their movement of solutions around the search landscape. Hyper-heuristics create a different challenge for explainability as they make use of many more operators, or low-level heuristics and learning algorithms which modify their probability of selection online. This paper describes a set of methods for explaining hyper-heuristics decisions in both online and offline scenarios using selection hyper-heuristics as an example. These methods help to explain various aspects of the function of hyper-heuristics both at a particular juncture in the optimisation process and through time. Visualisations of each method acting on sequences provide an understanding of which operators are being utilised and when, and in which combinations to produce a greater understanding of the algorithm-problem nexus in hyper-heuristic search. These methods are demonstrated on a range of problems including those in operational research and water distribution network optimisation. They demonstrate the insight that can be generated from optimisation using selection hyper-heuristics, including building an understanding of heuristic usage, useful combinations of heuristics and heuristic parameterisations. Furthermore the dynamics of heuristic utility are explored throughout an optimisation run and we show that it is possible to cluster problem instances according to heuristic selection alone, providing insight into the perception of problems from a hyper-heuristic perspective.