After a panicked rush to the top of the tower, Jyn manages to transmit the plans, and the rebels damage the shield, so they can receive them. The Death Star fires a low power blast at the planet, destroying the tower (and killing Orson Krennic in the process). Most of the rebels are already dead, and the few survivors are killed by the oncoming blast, including Jyn and Cassian, their mission complete.
The rebels in space copy the plans to a card as Darth Vader arrives and starts slaughtering his way through them to retrieve the information - they're trapped behind a door but manage to get the card out and onto a ship, the Blockade Runner from the start of Episode IV, which breaks free of its "parent" and makes a break for it. We see the plans get delivered to Princess Leia.