These are not eggs; they're actually galls, which are tissue swellings or malformations on plants that can be caused by a range of factors. Despite looking alarming in some cases, or just being very numerous, most galls cause no significant harm to the host plant. In this case, they may be mite galls, and determining which type depends on the host plant (looks like a Black Tupelo tree, perhaps). You can learn more about this type of gall in Ohio State's article "Bladdergall Enlightenment," which happens to include a Black Tupelo example. No action needs to be taken, and the galls may or may not reappear in a future year when the tree leafs-out again after winter. If the leaves it sheds this year are raked-up and disposed of, there might be reduced risk of recurrence, though it's not a foolproof approach.

Miri