implies that you pretend to do/be something.
頑張って強そうなふりしてるだけだ。 He's trying his best pretending to look strong.
見てみぬふり is a very common set expression meaning that you pretend not to have seen something (turning a blind eye)
警察官はそれを見て見ぬふりをする。 The police officer pretends not to see it.
この蛇は人など大きな動物が近づけと死んだ振りをするらしい。 I heard that this snake pretends to be dead when humans and bigger animals approach it.