What makes a US 2 dollar bill rare?

The criteria for rare $2 bills are basically the same as that for any US banknote: its date, its condition, what letter if any is next to the date, and in some cases its seal color.

As a rule of thumb just about every $2 bill printed before 1928 is worth a moderate to significant premium, but you won't find one in change because they were issued as large-size "horseblanket" bills that no longer circulate.

$2 bills dated 1928 through 1963 are the same size as current notes but were printed with red seals. That makes them so unusual they're effectively no longer in circulation either. Most aren't very valuable but ones to look for at estate sales, etc. would be 1928 A and 1928 B.

Other 1928, 1953, and 1963 $2 bills are quite affordable with prices in the $5-$50 range.

Finally, any modern green-seal $2 bill is just an ordinary Federal Reserve Note worth only two bucks. Feel free to spend any and all that you get. They're interesting to use and save money for taxpayers because each bill does the work of one $1 bill.