An e-receipt is the same as a paper receipt, but is emailed to you rather than printed out in store. Stored in your inbox, you will never lose a receipt again!
Email receipts usually appear in your inbox within 2 hours of the transaction (usually much sooner!).
When you make a purchase in store, the staff member will ask you if you wish to receive your receipt via email, and if so, they will enter your email address into the till system.