To reset progress in Osmo apps (except for Monster), click on the settings icon (a gear) in the top left corner of the home screen and select 'Reset progress'.
As for Monster, the developers are working on a reset feature, which should come in a future version. Currently, the only way to reset Monster is to delete and reinstall the app.
We're working on adding better functionality for teachers. If you need to reset progress on a long list of profiles, the best solution right now may be to delete the old profiles and create new ones.
You can delete student profiles at your myOsmo page (https://my.playosmo.com).
After you log in, click 'myProfiles' on top of the page, then select the profiles you wish to delete and click 'Delete'.