According to the BABOK® v3 guide, the purpose of Trace Requirements is to do the following:
"…ensure that requirements and designs at different levels are aligned to one another, and to manage the effects of change to one level on related requirements."
So, ultimately, the purpose of requirements traceability is to trace where each requirement or design comes from or originated from and what its life cycle is throughout the project.
If it is known why a requirement exists, or where it originated from, it will ensure that once the solution has been delivered, it does in actual fact solve the original requirement.
By knowing where a requirement came from, or what the need that should be addressed is, the business analyst will know who to communicate to as well as be able to manage the risk, scope, and any changes associated with that requirement.