Large language models (LLMs) have exhibited remarkable capabilities in learning from expla- nations in prompts, but there has been limited understanding of exactly how these explana- tions function or why they are effective. This work aims to better understand the mechanisms by which explanations are used for in-context learning. We first study the impact of two dif- ferent factors on the performance of prompts with explanations: the computation trace (the way the solution is decomposed) and the natural language used to express the prompt. By per- turbing explanations on three controlled tasks, we show that both factors contribute to the ef- fectiveness of explanations. We further study how to form maximally effective sets of expla- nations for solving a given test query. We find that LLMs can benefit from the complemen- tarity of the explanation set: diverse reasoning skills shown by different exemplars can lead to better performance. Therefore, we propose a maximal marginal relevance-based exemplar selection approach for constructing exemplar sets that are both relevant as well as comple- mentary, which successfully improves the in- context learning performance across three real- world tasks on multiple LLMs.