I found my dad's certificate which says "Sandan" on it.
What does that mean?
Is it a 3rd degree Black Belt?
Yes, Sandan means 3rd dan, or third degree black belt.
In rank systems patterned after the Japanese, dan (black belt) ranks count up:
A sandan rank is higher than a shodan or nidan rank and lower than a godan rank.
The kup/kyu ranks count down. A first kyu is higher than a second kyu.
It probably refers to "third Dan" in Korean.
When numbering the dan ranks, Sino-Korean numbers are used (rather than traditional Korean numbers). In other words, the ranks are il dan, ee dan, sam dan, etc., not hana dan, dool dan, set dan...
While Sam is usually used as the romanization for the sino-korean Three, they can vary and San could have been used in this case.
To elaborate a little, the term "Sandan" is written in Chinese characters as 三段 (Sān duàn, while Sandan would be the Japanese reading), or Korean as 삼단 (samdan).
三/삼 is the number Three (3);
段/단 refers to grades, steps, or stairs.
As such this term refers to something like the third grade, and refers to the third grade or degree of black belt in most modern Asian martial arts.
(Prior to this system the closest there was to a grading system was a certificate system).