What is the diffuse ionized gas?
The "diffuse ionized gas" (DIG) is another term for the phase of the interstellar medium (ISM) usually called the warm ionized medium (WIM). With a temperature of the order $10^4\,\mathrm{K}$, but extenting to lower and higher temperatures, it is hot enough to keep hydrogen ionized, and various metals exist as low-ionization species, such as S II, N II, and O II, and even (weak) O III (e.g. Hill et al. 2012; Zang et al. 2017; Weilbacher et al. 2018).

Rough pressure equilibrium with the other phases of the ISM results in characteristic densities of $0.1\,\mathrm{cm}^{-1}$, but typical ranges are an order of magnitude to both sides.

A review of the DIG/WNM can be found in Haffner et al. (2009).