When fighting other players, you receive Conquest points. You can invest these points into upgrading your Specialists or modernizing your whole army by researching relevant Technologies in your Academy in the City.
Please note that when defending your City from an attack, you will usually receive fewer Conquest points than the attacker.
There are other sources of Conquest points, for example, Arenas, achievements, and some tournaments (e.g., Shadow Invasion or Clash of Kingdoms).