What are the squiggly lines on my Aquilegia leaves?

They are made from an insect larvae called a leaf miner. This larvae which can be from a sawfly, moth, or other insect is a general term for insect larvae that eats the tissue of leaves. Pesticides usually kill insects and not larvae so spraying is not going to solve the issue.

Is the leaf miner a threat to my Aquilegia plant?

No. I have had leaf miner on almost my Aquilegia plants each year and the plants still grow and thrive. However, if you experience this on plants, shrubs, or vegetable plants, I would removed the infected leaves and dispose of them in the garbage NOT compost. In my experience I have never had a plant die that was infected with leaf miners but on crops you may not want the unsightly larvae eating edibles.