If you wonder what this all means, I will try to explain. Luminosity is a measure of the amount of particles you get to collide with other particles in a small region in the core of your detector. By circulating more particles in the beams, and by squeezing the beams to be as narrow as possible near the interaction region, you can increase the rate of their collisions. This is exceedingly important for a discovery machine, which needs to study very rare processes and thus is critically dependent on the maximization of the number of collisions that get produced.
With the new record, comes of course a good bunch of new data for researchers to analyze. Of course analysts want as much "integrated luminosity" as possible, and they would actually not mind if the "instantaneous luminosity" were smaller. To get the former, you need to integrate the latter in the time of the data taking; since instantaneous luminosity decreases quickly after beams start to collide (due to particles being removed from the beams when they collide, or because of small losses during their travel in the beam pipe), the peak luminosity -what makes the record today- is not the only important parameter in determining how large is the total size of analyzable data that get eventually collected in the data tapes. Further, the higher instantaneous luminosity comes at a price: more protons are collided in the same instant, with a correspondingly harder job for physicists to figure out what exactly happened in the "event" they study.
In any case... Way to go, LHC!