In parliamentary democracies, the "government" is the term used for the ruling party or coalition. Even more specifically, it's used for the Ministers. It's a more specific term than just referring to all elected representatives sitting in the parliament (the Bundestag, in the case of Germany, or maybe the Bundestag & Bundesrat). Comparing it to the American system, "government" is somewhat analogous to the "executive"—the President and Cabinet Secretaries—except that it's a fuzzy term and can also mean the non-ministerial members of parliament who are allied with the ministers.

So the AfD will not be a part of the Government because both the CDU/CSU and SPD have placed a cordon sanitaire around the AfD. They refuse to work with them because they view them as dangerous extremists. It would be theoretically possible for the CDU/CSU to break that cordon and form a government between just their party and the AfD, or they can form a traffic light coalition with the SPD and Green party. The latter seems more likely, given recent German political history.