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In terms of circumferences, we are only upgrading from 27km to 100 km. Only a factor of 3 :)

How does this extra distance allow for seeing things not possible with the smaller LHC? This is probably a really dumb question... Is it just because greater velocities can be achieved?

The extra distance allows us to accelerate the particles further.

The LHC will act as a pre-accelerator and the beam will then be injected in the new ring where the kinetic energy of the particle is expected to be multiplied by 7.

If this new ring is ever built of course (let's hope) :)

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