A turn starts when you send something and ends when the agent stops and hands control back. In between it may think, call tools, read files, run commands and think again. All of that is one turn, however long it took and however many round trips it made internally.
Why the unit matters
Counting messages tells you nothing: one message can be a typo correction and the next can be forty tool calls. Counting tokens tells you the size but not the shape. The turn is the only boundary where all three questions line up: what did it cost, how long did it take, how much bigger is the context now.
It is also the unit a person actually experiences. "It took three turns" is a real sentence about how the work went. "It took 180,000 tokens" is not.
What a turn costs
Four things, and only the first is obvious. The input is everything resent this turn: system prompt, tool definitions, whole history. The reasoning is however much thinking was asked for, which is what effort level decides. The output is what came back, priced higher than input and never cached.
The fourth is tools, and it is the one that catches people out.
Reading a large file into the conversation is not a one-off cost. It is now part of the context and you pay for it on every subsequent turn until something compacts it away.
Cost is recorded per message and per task, so "what did this turn cost" is a number you can look at rather than a share of a monthly total.