The big difference between a dedicated banking app and the one in the browser is permissions.
It sends me notifications when money arrives or is spent. Scanning a QR code to pay for something is much less clunky than doing the same in a browser. And it integrates into my phone authentication system so I only need to scan my fingerprint to open the app instead of remembering a password and waiting for a one-time code.
What do I do on the app? I check the balance on my accounts, I move money between my accounts to get more interest, I pay for my kid's remedial classes, I pay my trainer, I scan QR codes to pay online when the shop provides this payment option so I don't have to type in my card details, I check my virtual card details when I do have to enter them, I buy and sell stocks.