Cost is mainly due to fuel consumption. Concorde was extremely efficient in cruise mode, but horrible during the takeoff phase. And unfortunately, at takeoff it was also the heaviest, having full tanks, so the problem was compounded.
If a new design can solve the takeoff problem, then you actually solve four problems: overall fuel consumption (so lower cost), less pollution (because you burn less fuel) are two. The other two come from the ability to efficiently fly subsonic, which is what Boom claim to be able to do (when they'll be able to fly, obviously). You don't have noise, and you have access to some routes that are partially overland. For example, you could fly from NYC to various cities in Europe other than London and Paris. Maybe Frankfurt, or Berlin, or Madrid, or Rome. 90% of the flight will still be over water, but you can have 10% over land without producing the sonic boom.
