Genetic Algorithms have established their capability for solving many complex optimization problems. Even as good solutions are produced, the user's understanding of a problem is not necessarily improved, which can lead to a lack of confidence in the results. To mitigate this issue, explainability aims to give insight to the user by presenting them with the knowledge obtained by the algorithm. In this paper we introduce Partial Solutions in order to improve the explainability of solutions to combinatorial optimization problems. Partial Solutions represent beneficial traits found by analyzing a population, and are presented to the user for explainability, but also provide an explicit model from which new solutions can be generated. We present an algorithm that assembles a collection of Partial Solutions chosen to strike a balance between high fitness, simplicity and atomicity. Experiments with standard benchmarks show that the proposed algorithm is able to find Partial Solutions which improve explainability at reasonable computational cost without affecting search performance.