You can select multiple emails with the checkbox to the left of each email and then tap on the delete button to delete the selected emails.

You can also select all emails in a folder with the ✓ button at the top of the screen. Then tap on the delete button to delete them all.

Double tap on the ✓ button at the top of the screen to open all threads and select all emails.

To open all emails hidden in closed threads, you can also select the "Open all threads" item in the action menu. (circle with 3 dots button)

You can also double tap on the checkbox of the top thread email to open the thread and select all emails inside one email thread.

You can also do a long tap on the delete button to choose to delete emails from the email server instead of sending them to the trash folder.

You can also perform other actions on multiple emails such as 'Mark as Read', 'Move to mail folder' etc. Use the action menu (circle with 3 dots button) after selecting emails.

To select some emails to delete, such as older than a date, you can do this.
Tap on the search button to show the search bar and then tap on "More/..." to show the advanced search (View). Then tap on the "+" button to add a new search field for the date of an email, select the "Before" comparison and enter the date you want. Delete any other filters with the trash button.
Do the search and then tap on the ✓ button at the top to select all emails and then tap on the delete button.