The Center for Theoretical Cosmology explains the Hartle-Hawking state as follows:

One can picture the spacetime of an expanding Universe as the surface of a cone, placed vertically with its sharp tip down. Time runs up the cone: space runs around it. Time and space end at the sharp tip. The tip is 'singular' in mathematical terms and if this were a model of the Universe we would find all our equations break down there. Instead, Hartle and Hawking proposed that the tip be rounded off.

This rounding off is only possible if the nature of spacetime changes in the vicinity of the tip. In effect, all directions must become 'horizontal' near the tip, which is to say that all directions are spacelike. This is just what we need to explain how time began. In effect the distinction between space and time is blurred and space is then rounded off.[1]