The answer is: Because it's in a bound state, and all bound states have negative energy relative to the unbound reference state.
Two objects are usually defined to have zero potential energy relative to each other when they're so far apart that their interactions are negligible-strictly speaking, they're taken to be infinitely far apart. This is the unbound reference state, the state that's usually defined to have zero energy. If they repel each other, as you move them closer together it takes work to do this, and the potential energy is positive. But if they attract each other, as they move closer together the potential energy goes lower and lower. And since it started at zero, the potential energy is negative.
The electron also has kinetic energy, but it's smaller in magnitude than the potential energy (by a factor of 2 for a hydrogen atom; it comes from the inverse-square law). So the total energy (kinetic + potential) is negative.
All it's saying is that you'd have to add energy to it to bring it to the reference state, in other words, to remove the electron from the atom.