Each call to the Google Apps Script web app is handled by an independent execution.
An independent execution handles each call to Google Apps Script server-side functions using google.script.run.
Above, I'm using independent for emphasis purposes. From a language economy perspective, execution should be enough.
All Google Apps Script executions are logged in the Google Apps Script's project execution log, which can be seen by anyone with access to the Google Apps Script project and the related Google Cloud Platform project.
How organization admins might have access to the execution logs depends on several factors, including but not limited to the Google Workspace edition used by the organization.
Note:
If you are planning a web app, please be aware that there are limits to the number of simultaneous executions per user and per script. For details, see https://developers.google.com/apps-script/quotas.
Resources
Resources that mention stuff that might help to understand what is execution in Google Apps Scripts
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Extracts from the above link:
Executions. The number of times a project has been "run" or executed. See Execution types for more information about how a project can be run.
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Manage executions
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The Type column shows what initiated the execution. Values include:
- Add On. The execution originated from an add-on.
- Execution API. The execution originated from an invocation of the Apps Script API.
- Time Driven. The execution was caused by a time event.
- Trigger. The execution originated from a trigger source.
- Webapp. The execution originated from a deployed web app.
- Editor. The execution originated from the Apps Script editor.
Logging From the above link:
A basic approach to logging in Apps Script is to use the built-in execution log. To view these logs, at the top of the editor, click Execution log. When you run a function or use the debugger, the logs stream in real time.