The performance of Large Language Models (LLMs) on downstream tasks often improves significantly when including examples of the input-label relationship in the context. However, there is currently no consensus about how this in-context learning (ICL) ability of LLMs works: for example, while Xie et al. (2021) liken ICL to a general-purpose learning algorithm, Min et al. (2022b) argue ICL does not even learn label relationships from in-context examples. In this paper, we study (1) how labels of in-context examples affect predictions, (2) how label relationships learned during pre-training interact with input-label examples provided in-context, and (3) how ICL aggregates label information across in-context examples. Our findings suggests LLMs usually incorporate information from in-context labels, but that pre-training and in-context label relationships are treated differently, and that the model does not consider all in-context information equally. Our results give insights into understanding and aligning LLM behavior.