The basic objective of the project is to provide a true northbound platform, so that NB passengers won't have to walk over the southbound tracks to get on a train.
This is both for safety (someone might step out to catch a NB train and not notice an approaching SB one) and for scheduling convenience. A SB train can't pass through while an NB train is in the station (or really, for the reason of the safety concern I just mentioned--any time an NB train is in sight). This is called the "hold out rule". The NB platform will be accessed via a pedestrian tunnel, currently being dug at the south end of the platform.
Anyway, a lot of this you can probably guess from just looking at the site, but some details are not obvious. What will things look like when it's all done? Will the new NB platform connect with the existing pedestrian tunnel that crosses under both the tracks and Central Expressway/Alma? It would be a pain for anyone living in the neighborhood over there, who wanted to catch a northbound train, to have to use two tunnels.
Turns out there's a more detailed factsheet about this project, which isn't linked to from the main site. And it's got pictures!
I can't tell from the project description or drawings whether it'll be possible to get to the NB platform from the existing tunnel under Alma. But it does look like gate-protected crossing of the tracks will still be allowed. I had been expecting the redesign to eliminate direct crossing of the tracks entirely, in the name of safety, and am glad to see that CalTrain is wiling to strike a reasonable balance between safety and convenience. (Besides, even in the suburbs, tunnels are creepy at night).
All in all, it seems like a fairly well planned project. I still have one one question, though--if all this work is costing $13 million, why is the (apparently) much simpler rehab of the Burlingame station taking $20 million?