to stick into and move around; to dig around in; to pick (i.e. one's teeth)
「抉る」 has other readings with different meanings.
爪楊枝で歯を抉った。
I picked at my teeth with a toothpick.
子どもが南京錠の鍵穴を細い棒で抉っていた。
The child was poking around in the padlock keyhole with a thin stick.
木の棒で土を抉ると貝殻が出てきた。
When I dug into the soil with a stick, a shell appeared.