What does "holy thing" refer to in Leviticus? In Leviticus 22:10 (and mentioned in a few other verses too) it says "...shall not eat of a holy thing..."

What does "holy thing" refer to?
"Holy" = "Set Apart (for a Special Purpose)"

"Holy" (qodesh, 6944 קֹדֶשׁ ) means "set apart (for a special purpose)." Its synonyms, like "consecrated" and "sacred" mean the same thing.

In the context of Leviticus 22:10, God is speaking of sacrifices.


  be careful with the holy gifts of the sons of Israel, which they dedicate to Me


Many of the sacrifices that the Israelites were to make gave a portion to the priests and Levites. (Ex 29, Nu 18) These were only to be eaten by (ceremonially clean) priests and levites. They were "holy" because they had been given to God.