Dear Student ,
The significance of the negative energy is given as under.
When electron is at the infinite distance from the nucleus there is no force of attraction between the electron and the nucleus. therefore the energy of the electron is assumed to be zero.
When electron moves closer to the nucleus it does so by itself under the attractive force of the nucleus. In doing so, it consumes or spend some of its energy. therefore energy of the electron becomes less than zero.
Hence the energy of an electron in an atom is negative. When it moves more closer to the nucleus energy of the electron becomes more negative.
Regards