Plain English Meaning
When you turn at a fix, your aircraft swings through a wider piece of sky than when flying straight. At some fixes, that extra space contains terrain or obstacles. Minimum turning altitude is the higher altitude you must be at to safely complete that turn.
Full Definition
A published altitude that ensures safe terrain and obstacle clearance during a turn at certain en route fixes or NAVAIDs, where the standard minimum en route altitude does not provide adequate clearance for the larger area an aircraft sweeps through during a turn.
Context Anchor
Seen on instrument procedures and route segments where a turn at a named point needs extra altitude for safe clearance.