Short for excited state multimer
An excimer is a complex formed between several (usually two) of the same fluorophores in the excited state. When a molecule is excited, the density of electrons shift. This may allow certain molecules to stick together where they couldn't before. Sometimes, due to mixing of the molecular orbitals, the excimer will fluoresce at a new wavelength separate from the emission of the single molecule.
A classical example is the dye pyrene, which will form an edge-to-edge dimer with another pyrene molecule when excited, giving it a redshifted emission. This is taken advantage of in protein chemistry. If one is interesting in ascertaining whether two proteins stick to each other, one can chemically attach a pyrene to specific sites on each of them. Since the pyrene is tethered onto the protein, it can only form an excimer with another pyrene if the two labeled proteins are sticking together in a way that the two dyes are within molecular contact distance of each other. Its a useful technique when other methods of structural characterization fail.
See also: exciplex