There are many possible ways to define the goals and concerns of the modern Islamist movement. One possibility is to say that this movement is an attempt to bring about a Muslim world that is politically united under Islamic religious law.
If we look at Islamism in this way, we can see that many countries around the world have instituted some aspects of Islamist ideas. For example, countries like Saudi Arabia and Iran place various restrictions on what women may or may not do. These restrictions are based on their views of Islamic law. As another instance of Islamism, countries like Pakistan have very stringent laws against Muslims leaving the faith (apostasy).
By this view, then, Islamism is an attempt to create a Pan-Islamic society that would be ruled not by secular and nationalistic leaders, but by religious leaders who are committed to Islam before their separate countries.