Background pollution is what would be measured if no anthropogenic emissions existed. In other words, if you shut off human activity (or avoid the emissions from it), you can measure the background. Sometimes this is called the natural background. There are also regional backgrounds, like "the US background", which additionally includes anthropogenic sources from outside the region. In order to measure background concentrations, you need to be in a remote area that is not influenced by human activity (e.g. see "Influence of background particulate matter on urban air quality in the Pacific Northwest" by Timonen et al., 2013).
Background concentrations of particulate matter can approach zero in pristine areas, but will be seasonally influenced by natural events like wildfires and dust storms. Background NOx also approaches zero in pristine areas but can be perturbed by lightning generation and soil processes. In contrast, background concentrations of ozone can rise naturally without an emissions source, especially in mountainous areas that are exposed to air from stratospheric intrusions. Ozone is one of few the air pollutants whose background concentrations are significantly influenced by sources not at the surface.
Using an air quality model, a researcher can "zero-out" anthropogenic emissions in order to estimate the background. There are also source-apportionment techniques that can be used to estimate the background (see "Comparison of background ozone estimates over the western United States based on two separate model methodologies" by Dolwick et al., 2015).
You might enjoy this white paper that the EPA recently released about the complexities involved with estimating background ozone.