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:
[ This is a work in progress, feel free to make suggestions ]
(LR) - Book (SR) - Pamphlet (A) - Article
What is Anarchism?
At The Cafe - Malatesta (LR)
Are you an Anarchist - Greaber (A)
The ABC of Communist Anarchism - Alexander Berkman (LR)
Anarchism in depth
The Conquest of Bread - Peter Kropotkin (LR)
God and the State - Michail Bakunin (LR)
The Anarchist FAQ - AFAQC (LR/SR)
Black Anarchism
A Black Autonomy Reader - Mutt. (LR)
Anarchism and the Black Revolution - Lorenzo (LR)
Ecology and Environmentalism
The Solutions Are Already Here - Peter Gelderlous (LR)
Worlds End - Mycelium Collective (SR)
Ecology of Everyday Life - Chaia Heller (LR)
Capitalism is Killing the Earth - Anarchist Federation (SR)
Feminism
Feminism is For Everybody - bell hooks (LR)
Throwing Like A Girl - Iris Young (SR)
Sex Slavery - Voltairine De Cleyre (SR)
Housing / Society
Bolo'Bolo - Hans Widmer (LR)
The Hidden History of Housing - Colin Ward (SR)
Indigenous Anarchism
No Spiritual Surrender - Klee Benally (LR)
Organising
The Role of the Revolutionary Organisation - Anarchist Federation (SR)
Social Anarchism and Organisation - FARJ (SR)
Police & Prisons
Seven Myths about the Police - CrimethInc. (A)
Queer & Gender Studies
Queer Ultra Violence - Various (LR)
Solidarity Economics