When people say that humans are "basically good," they might mean any of a few different things.
Some people might mean we are "created this way" by God, but a more scientific worldview can also attempt to identify intrinsic goodness. Social animals have to support each other or the group will not survive. This is studied in evolutionary biology. The term "reciprocal altruism" is used especially when some form of payback is expected — "you scratch my back and I'll scratch yours”. A specific act may be done without expectation of reward, but the general rule holds true. Even "random acts of kindness" strengthen a society by distributing resources and building trust, so the giver benefits in a less-defined but still tangible way.
Some empathy happens unconsciously because we have evolved to have those feelings, but some surely happens more intentionally. When we simply want something, philosophers call it a "first-order desire"; when we "want to want" something, it's a “second-order desire.” "Wanting to want" means we're critiquing and intentionally developing our own desires. (e.g. One might say: “Typically I’d rather mind my own business than reach out to a stranger, but I want to become the kind of person who is nice to strangers.”) To this end, we study philosophy, join groups (consider organized religion), and pay each other (consider customer service representatives) to be more pleasant and helpful than we would naturally be without those social supports.
Usually good (in practice)
People who make this claim are saying that — regardless of whether we are born good or choose to be good — we are kind and supportive to each other far more often than we are cruel and destructive. Consider how fragile trust is, and how, every time trust is breached, it takes a hundred or a thousand kind acts to rebuild it. We remember the times people hurt us, while we tend to overlook the thousands of times people are directly kind to us and the millions of ways they have been indirectly supportive from a distance. Though it may sometimes be hard to remember how many times people have been kind to us, a simple inventory will demonstrate this.