Because the body and the mind are not only connected, they are different facets of the same thing. Every aspect of one is reflected in the other.
In tai chi, we say that everything physical has psychological analogues, and everything psychological has physical analogs. What shows up in your practice shows up in your life, and vice versa.
If the body becomes rigid during meditation, so will the mind. A flexible body corresponds to a flexible mind.
From another perspective, physical movement propels circulation, of both blood and lymph as well as chi.
Finally, all meditation centers on breathing. If the body is fluid, the breath moves throughout it. Restricting the body in any way automatically restricts breathing.