A risk register is a record of risks. In addition to listing the potential problems for the project, the register may have a title and/or identifier for each risk, the likelihood of the risk occurring, elements of the project that will be affected, the expected severity if the risk occurs, a prioritization (usually based on a combination of likelihood, severity, and potentially adjustments by leadership). It is sometimes called a "risk log". Not surprisingly, the risk register is an output of the PMI process, identify risks.
When a process results in project documents updates, one of the documents that may be updated is the risk register.