One of the cool things about anarchism (that also makes it tricky to define) is that it has different interpretations, it has a certain fluidity. Pretty much everyone agrees though that practicing anarchy is about trying to minimise coercion, domination and hierarchy in the world. Capitalism and the state (made up of the government, courts, police etc.) are seen as systems that fundamentally maintain such domination, and anarchists hate that shit. Anarchists also fight against all forms of inequality and oppression in society, such as sexism, racism, ableism and homophobia.
Many anarchists like to talk about anarchy as constantly evolving, with no fixed end goal, more like a continual striving for emancipation. A journey not a destination.
If you want to find out more, here's a few suggested readings: