Plan check is when your building plans are reviewed to make sure they comply with basic safety, engineering and planning rules. LADBS plan check engineers will review the design of such things as the structure, plumbing and electrical systems to make sure they are safe and properly designed. They will also look at other items, like building setbacks, heights and lot coverage to see that the construction is compatible with the neighborhood.
Plan check is part of the permit process. If your project disqualifies you from directly receiving an Express Permit, you will need to have a plan check. If it's a small project, a Counter Plan Check will suffice. If it's a large project, you might need to have a Regular Plan Check, where your plans are submitted and reviewed over the period of several weeks.