Offline access to Airtable is not currently possible, however there are several options available for exporting your data to access it offline.
If you'd like to save your current Airtable records offline, you can export data from Airtable as CSV files. Note that you will need to export attachment files separately. Each table in your base will need to be downloaded as its own CSV. Note that exports do not include record-level comments, app content, or base / field description.
Another backup option would be to set up an API integration that could periodically fetch all your data and save it, although this would involve some advanced program. You can find API documentation specific to your bases at airtable.com/api.