I'd like to add the clarification that color is how our brain interprets light's wavelength. So 'blue' and 'short wavelength' mean the same thing, when talking about light.

The laser in a DVD or Blu-ray drive is used as a 'needle' to detect small pits on the disk, which encode 1s and 0s. A red laser has a long wavelength and is akin to a fairly blunt needle. It won't detect very small pits, so the pits in the disk need to be fairly large. Which limits the storage capacity of the disk.

With a blue laser, which is a much finer 'needle', the pits can be a lot smaller, so a lot more data can be stored on the disk.

There are also other factors like how fast the disk spins, and how close the pits can be to eachother. The accuracy of electronics manufacturing has improved since the advent of dvd's, so we can now make smaller devices with fewer chances of important errors. How efficiently the data on the disk can be compressed has also evolved substantially since the advent of DVD, further increasing the amount of video a disk can hold.