Hydrogen-like ions are ions that possess only one electron, just like a hydrogen atom.
The fact that these ions have only one ion in the outermost shell makes it simpler to analyze their radii and energies, as a simple electrostatic model can be used to describe them. Species having multiple electrons are difficult to study and are beyond the scope of the Bohr model. This is because the inter-electronic repulsions are hard to account for in electrodynamic interactions that make up the atom's bound system.
