From the app's home screen, tap on the Ethereum wallet the transaction was made from.
You should then see a list of transactions. Tapping on a transaction will display more details, such as whether the transaction has been confirmed or is still pending.
If you tap "View transaction on block explorer," you'll be taken to etherscan.io, where you view even more details for the transaction. For example:
The "Transaction Hash" is the identifier for this transaction. Every transaction has a unique hash. If the status is "Pending," your transaction still hasn't been picked up by a miner. Assuming the gas limit and gas price you've set for your transaction is sufficient, it will eventually be added to the blockchain by a miner, at which point the screen will auto-refresh with your status updated to "Success" and show the number of block confirmations: