You often hear intergalactic space is an example for a very good vacuum. But how vacuos is space between galaxy clusters and inside a huge void structure? Are there papers quoting a measurement/approximation method (building the difference of a very near known and far away similar spectral source)? Are the rest particles mainly Hydrogen, He,...? Is it important at all to know the average density of intergalatic space in cosmological research?
According to Universe Today, for the intergalactic medium they state a figure of only one hydrogen atom per cubic meter. As a point of comparison, the University of California, San Diego quotes an interstellar density of 1 atom per cubic centimeter.
As to why it is important, all this material has photoionization effects on observations. Even though it is incredibly diffuse, because temperature is defined by the excitement state of atoms, this intergalactic medium is millions of degrees! This level of excitation could cause you to get erroneous results if you do not compensate for it. There is a review article by Piero Madau that explains it much better than I can. That probably explains a great deal more than I could here, although it will require quite a few pages of reading.