I think it's because less energy is required by the nucleus to keep them in orbit around it, hence they have a low energy level, making them more stable than those further out from the nucleus.
Really have forgotten though so if I'm wrong someone please correct me
From what I think/remember - the nucleus of an atom is inherently positively charged (since protons are positive and neutrons have no charge), therefore since electrons are negatively charged: there is an electrostatic force of attraction between the nucleus and the electrons.
So how I think of it is, think of a magnet and a piece of metal: it's 'natural'/takes minimal effort and energy for the magnet and metal to be attracted and therefore close to each other, but it takes effort and energy to pull the magnet and metal apart from each other.
So in sort of the same way, if you pull the electrons that all want to be close to the nucleus (in the 'inner shell'/ground state) farther away from the nucleus (to outer shells) it takes more energy and are therefore at 'higher energy levels'.
Does that make sense?
(Feel free to correct/improve my flawed analogy or clarify if I've misunderstood anything!)