It is unlikely, though not impossible, that parliament will stop Brexit altogether.
However, they can ensure that we do not have a "hard" (or what I prefer to call a "stupid") Brexit and that the needs of those who voted to remain are not forgotten.
There is no earthly reason to leave the customs union, there are real issues with the way the vote went in Scotland and Northern Ireland (and London and other cities), and Gibraltar needs to have its 97% remain vote honoured. If parliament needs to approve the process, it will (hopefully) be more sensible and rein the three crazy Brexiteers in.
It will also delay things which gives those EU citizens living in the UK more time to qualify for UK citizenship and vice versa and give people more time to plan. Even if the delay is only 3 months or so, that could have an impact on quite a few people.