In this context, "broad" is a buzzword, a piece of scientific jargon. It's a callback to Broadly Neutralizing Antibodies[1], bNAbs. The basic idea with bNAbs is that they target parts of viral proteins that tend not to mutate or change very much between individual strains of some particular virus.
# Edit:
To clarify, I am not suggesting that an antibody with "broad cross-immunoreactivity" is the same thing as a bNAb. Immunoreactivity and neutralization are not the same thing (although there is some overlap).
> 1: Zwick, M. B., Labrijn, A. F., Wang, M., Spenlehauer, C., Saphire, E. O., Binley, J. M., et al. (2001). Broadly Neutralizing Antibodies Targeted to the Membrane-Proximal External Region of Human Immunodeficiency Virus Type 1 Glycoprotein gp41. Journal of Virology, 75(22), 10892–10905. <