The heel is the back of the foot. And to dig is to go deep into the ground. This expression sounds as if Anna and Jonathan are walking heavily.
dig your heels in 坚持己见,一意孤行
Jonathan: Our work party(团建) is going to be at a skating rink(溜冰场)?
Anna: Yes. Olga planned it this year and that's what she wants.
Jonathan: But not everyone in the office can roller skate(轮滑). Why not do something everyone can enjoy?
Anna: I agree. But when Olga digs her heels in, there is no changing her mind.
If you dig your heels deeply into the ground, you could be very hard to move. People who dig their heels in refuse to change their opinions or plans. In other words, they are very stubborn.