This creates a new transaction with higher fees but otherwise has the same addresses and payment amounts as the first transaction.
Specifically, this is called First-Seen-Safe RBF, or FSS RBF. This means that RBF can only be used if the new transaction pays all the same outputs as the first transaction by at least the same amount. It can pay more, it can pay additional outputs, it can spend additional inputs, it will obviously need a higher fee, but it must pay all the original outputs the same or more. You can read more about it here:
https://github.com/bitcoin/bips/blob/master/bip-0125.mediawiki#motivation. In reality, very few nodes actually enforce this, and most just use standard RBF as described by hosseinimr93 above.
More generally, there is also transaction malleability which allows a transaction to be modified after it has been broadcast. It will still spend the same inputs and pay the same outputs, but the transaction hash will be changed, which is why it is never safe to accept an unconfirmed transaction with one or more unconfirmed parents.