feigning illness; pretending to be sick
Almost always used in the pattern 病気のふりをする. Describes the act of pretending to be ill, often to avoid something.
See also: 振り (ふり)
He didn't want to go to school, so he pretended to be sick.
I don't want to attend the meeting, so maybe I'll pretend to be ill.
Common kana-mixed spelling; the ふり part is often written in kana for this meaning.
Kanji spelling for ふり is also used, but kana is more common for the 'pretending' sense.
Compound of 病気 (illness) + の (possessive particle) + ふり (pretending). The ふり part comes from 振り, meaning 'pretending' or 'feigning'.