The patient's condition is about to change.

Literal

Sick-person [possessive-の] condition [topic-は] is-on-the-verge-of-changing.

変わりかけている uses the compound auxiliary ~かける ('to be on the verge of, to start to') in its ている form, meaning 'is in the process of starting to change.' 容態 (ようだい) specifically means 'a patient's condition.'