I you're using the native Mail app, go to your inbox, select each item you want to delete, then select "Delete" or "Delete All". After that, go to your trash folder, select "Select All" and then select "Delete".
Go to your inbox> Tap "edit" in the upper right corner > mark each email to send to trash by tapping the white circles on the left side > Tap "trash" in the lower right corner > go to trash> Tap "edit" in the upper right corner > Tap delete all in the lower right corner.