Business keeps records for a variety of reasons; i.e. accounting, sales, inventory, etc. In safety records of safety training are very important for tracking who has been trained in what topics.
Being able to identify who was trained in what topics when is crucial for several reasons. First, you know who has been and who needs be trained in safety topics germane to your business. Second, the Occupational Safety Health Administration requires safety training in specific topics. That list can be found in OSHA Booklet OSHA 2254-09R 2915, Third, in the event you are sued for a workplace injury your safety training records, if well kept, can show your business takes safety seriously.
Safety record keeping, beats trying to remember everything.