An orphan transaction is a transaction that consumes a coin whose creating transaction is not known to your client. This has nothing to do with orphan blocks (which are blocks whose parent block is not known, or according to another definition, blocks that are no longer part of the best chain).

Orphan transactions are not part of a block (they cannot be verified until their parents are known, and only valid transactions are allowed in blocks), and are kept in memory in the client. When their parents become known, and they are found valid, they are moved to the memory pool (which is - as the name suggests - also kept in memory only). From there, they are considered to be included in new blocks (if you're mining).

This piece of debug.log tells you that there are 3 transactions received (separate transactions, not part of a block) that reference some inputs that aren't known. Because of this, they are stored in the orphan pool, which grows as a result of that. "mapsz" stands for "map size" (as the orphans are stored in a map) - the number is just the number of remembered orphans.