I'm reading a First Course in Differential Geometry by Chuan-Chih Hsiung and on page 8 he says "A closed disk that is homeomorphic to $I^2$ [i.e. $I\times I$, where $I = [a, b]$] is connected. The surface $S^2$ of a 2-sphere can be expressed as the union of two closed disks with nonempty intersection."
I'm not sure what he means by the second sentence. Am I supposed to imagine two disks being deformed into the two halves of the sphere (so the disks touch each other at their circumferences)? I don't understand what it means to express the spherical surface as a union of two disks.