I assume that the coach is referring to their American Swim Coaches Association (ASCA) certification. According to the ASCA website (www.swimmingcoach.org/.../coachpur.pdf):
There are three things analyzed in the Certification process. They are: Education, experience and Achievement. Your Certification shows that you have met the required standard at each Level. The Five Levels become increasingly difficult. Level 5 is composed of the top 2-5% of coaches in the USA. Level 4 is the top 5-8% and Level 3 is the upper 15% of coaches. Level 2 requires more units of education and experience than Level 1.
There are three key requisites necessary to qualify for Level 3 Education and Experience:
1. You must have been actively coaching for a period of ten full years (120 months), with at least six of those
years in a multilevel program where you report to a head coach. This program is not intended for Head
Coaches.
2. You must have completed the ASCA required schools through Level 3 and have a total of 175 educational units in your certification file.
3. A letter from the Head Coach in support of Level 3 Education and Experience must be enclosed with the
application. This letter should ascertain that the coach applying is not in a position where he/she is expected to
train athletes to upper levels of performance and is expected to provide foundation coaching.
Actually there is another type of level 3 certification. A coach can also be level 3 masters certification. The requirements are a little different and can be found here (www.macacoach.org/ascamasterscertification.pdf)
What it means I guess dpeends, but in general you can say that this is a person who has been coaching for a while, tries to stay current in the latest coaching methods and cares enough about it to a member of a professionsla organization.
Alas, it is not a guarantee that this person is a good coach. Nor that they are the right coach for you.
Most clubs have some sort of try before you buy arrangement or at least you can pay for a just a couple of workouts before you lay down a yearly membership fee.