Gmail

Log into Gmail from a browser on your computer. Go to the All Mail folder. Click the check box just above the email list. You'll see a notice that says something like "All 50 conversations on this page are selected. Select all 49,673 conversations in All Mail". Tap the second sentence to select all. Tap the trash can icon above the list of emails. Wait.

This is probably a question for the folks at Gmail assuming that you wish to use the same mail account. Or you could start fresh with a new Gmail account.