Why is the Hubble Telescope in space?

As @astromax observed, one of the primary factors that makes a space based telescope better than an equivalent telescope of the same size is scattering.

Along with scattering, there is also refraction which can be especially problematic when combined with atmospheric turbulence. In the modern era, this problem can be remedied to a certain extent using adaptive optics, but since the Hubble was designed, built, and launched before AO became practical in the 1990's, a space telescope represented the pinnacle of optical clarity for that time.

However, there is another important optical property of the atmosphere, absorption. Although the Hubble is primarily a visible light telescope, it does have instruments that cover both the near UV and near IR, both of which are absorbed by the atmosphere more than visible light.

Furthermore, there are practical advantages of space based telescopes. There is neither weather, nor light pollution in space.