Address reuse refers to the use of the same address for multiple transactions. It is a poor practice, as it reduces the amount of privacy that you and the receiving party of the transaction have. When addresses are reused, they allow others to much more easily and reliably determine that the address being reused is yours. Every time the reused address private key signs a new transaction, whoever receives it can use the histories of that address to discover information about you.
There has been significant research into the area of address reuse by different persons and companies. For example the The Open Bitcoin Privacy Project is an open source, global organization whose mission is to improve financial privacy within the Bitcoin ecosystem. They do annual reviews of Bitcoin wallets and provide data points on which wallet is the most privacy-centric, including which wallets promote address reuse or not.