A grammatical expression meaning 'cannot avoid (doing); must (do)'. It indicates that, due to obligation or circumstances, one has no choice but to do something.
明日は大事な会議があるから、行かないわけにはいかない。
There's an important meeting tomorrow, so I can't not go (I have to go).
親友に頼まれたことだから、断らないわけにはいかない。
Because my close friend asked me, I can't refuse (I have to say yes).
子どもが熱を出したので、看病しないわけにはいかない。
My child has a fever, so I have to nurse them (I can't avoid doing so).