What is this cable in my yard, why is it exposed, and what can I do about it?
That is a Homac 600V rated splice so it's probably part of your electric service. I would be calling the power company right now and report a dig in to an exposed  service or secondary lateral.
Stay away from it until the power company inspects it. It could be an abandoned line but you want to assume it's hot. It looks like a ground rod has been driven close by so maybe some old facilities have been relocated.