Destination Tags are used when a single address is receiving transactions from multiple users, like at an exchange. They are useful because, unlike Bitcoin, each XRP address needs to be initiated with a minimum 10 XRP deposit. This can quickly become expensive for an entity serving many users. Exchanges assign a unique Destination Tag to each user that the user includes with their deposit transaction. This enables the exchange to determine which user a deposit originated from.
To add a Destination Tag to an outgoing transaction from Edge, tap into the "Notes" field and add the desired note. Note, while exchanges may require Destination Tags they are optional and do not need to be included when sending a transaction from user to user.