I can't speak for the Mongols specifically. I can, however, speak for nomads in a more general sense. There are many instances of nomads having a central, permanent, location. This was used as storage, a center of trade, to house the weakest, and likely as a seat of diplomacy. A capital.

It is easy to think of nomads as borderless roamers. This is not the case. Nomads are often territorial, hugely so in fact. Still today in parts of Africa you will find violent conflict over territories among nomads. So there were borders of sorts, and nomads would often consider land theirs.

It's simply their subsistence relies on movement from place to place. They would take their herd of grazing animals, move from place A to place B. Spend months at place B before the seasons began changing and they would head to place C and stay there for months.

This lifestyle is believe to have existed at least as early as the Halafian culture, in the Levant (Neolithic). Probably earlier, I just happen to know of the Neolithic examples.

As you can imagine, having a centralized location is then hugely beneficial for all the reasons listed above. As I said, I don't know about the Mongolians specifically, but I can only assume they followed a similar tradition. Specially when you have an Empire, it would surely be near impossible to exert any kind of control if everyone was everywhere all the time.

Some Sources:

Tapper, R., 2008. Who are the Kuchi? Nomad self-identities in Afghanistan. Journal of the Royal Anthropological Institute, 14(1), pp.97–116.

Falah, G., 1989. Israeli state policy toward Bedouin sedentarization in the Negev. Journal of Palestine studies, 18(2), pp.71–91.

Abdul-Jalil, M.A., 2008. Nomad-sedentary relations and the question of land rights in Darfur: from complementarity to conflict. Nomadic-sedentary Relations and Failing State Institutions in Darfur and Kordofan (Sudan). Orientwissenschaftliche Hefte, 26, pp.1–24.

Di Cosmo, N., 1994. Ancient Inner Asian nomads: Their economic basis and its significance in Chinese history. The Journal of Asian Studies, 53(04), pp.1092–1126.

Akkermans, P.A. & Le Miere, M., 1992. The 1988 excavations at Tell Sabi Abyad, a later Neolithic village in northern Syria. American journal of archaeology, pp.1–22.