|How the sausage is made|
A political binary system in politics is the theory or practice that all of politics can be best (or only) expressed as a binary on a single axis, with people being more "a" or "b"—and attempting to attract voters or writing laws based on that single axis.
In the United States, for example, politics is typically portrayed as a conflict between "Left v. Right" or "Conservative v. Liberal", and only two parties (Republicans and Democrats) participate significantly in governance. The two parties identify along binary, polarized systems on several hot-button issues.
The effect of seeing politics as a polarized binary field is that any other possibility for organization is not given a strong voice, or even a place at the table, and most candidates must align themselves within the spectrum of that binary.
Simple examples as they play out in US politics, include issues such as "pro-Life" v. "pro-choice", where there is no real room to accommodate within the system someone who says "Hey, let's focus on reducing the number of unwanted pregnancies".
If the discussion is about taxes, the options are "tax more" and "tax less". Creative solutions which do not fit into that system do not fit into the binary and are not heard.
In addition, any politician who does not match the binary on all hot button issues is marginalized and voters who do not match are left out. No US politician on the national level can be pro-life and support gun control.
The rest of the West
Many other, if not most, Western countries mitigate the extreme sense of the polarization seen in the US, by having many active parties that are not founded on a single axis, but represent different issues (e.g. Socialist Workers Party, Green Party, Front National, New Republican Party, and the other Socialist workers' party).