The emission spectrum of a particle is the frequency of radiation given off in the form of electro-magnetic radiation as the particle returns from a higher energy level to a more stable level with a lower energy.
When atoms are excited by exposing them to electro-magnetic radiation, a part of the energy is absorbed. Atoms absorb energy by a change in the distance at which electrons orbit the nucleus. It is not possible for electrons to orbit around the nucleus at any distance; the orbital distance is constrained to discrete values each of which corresponds to a specific energy level. The emission spectrum of atoms has radiation of frequencies that correspond to the difference in energy between different energy levels of the electrons. These are limited in number as electrons only move between a few select energy levels. This results in a relatively simple emission spectrum of atoms.
When atoms combine to form molecules the number of energy levels between which the electrons in the atoms can move is increased greatly. In addition, molecules can absorb energy by undergoing other transitions like rotational, vibrational, and vibronic. This greatly increases the number of frequencies of light emitted by molecules in their emission spectrum. This is the reason why the emission spectrum of molecules more complex than that of atoms.