An LRS is the system of record for xAPI data. Whenever a learner does something trackable — "Maria completed Forklift Safety," "Sam passed the HIPAA quiz" — the activity sends a statement to the LRS, which stores it and makes it available for reporting and analysis.
An LRS can live inside an LMS or stand alone, collecting data from many sources at once. That is the key difference from SCORM: SCORM reports only within a single browser-launched course in one LMS, while an LRS can capture learning across mobile, offline, simulations, and on the job. See SCORM vs xAPI for the full comparison.
Related questions
Do you need an LRS to use xAPI?
Yes. xAPI statements have to be sent somewhere, and that destination is a Learning Record Store. Every xAPI setup includes an LRS, whether it is built into the LMS or run separately.