The definitions of 'liberal' that I find most relevant in parsing anarchist texts or anews comments (wait, in post-modernity do anews comments count as 'texts'?):
1. A synonym for bad. "That's so liberal."
The common, moral, definition, where the process of identifying evidence of liberalism, and leveraging it for dismissal, is an easy way to engage with a text or person. "Ah, this is liberal, well then it's settled." If I were to be generous to the anarchist usage of this first definition, I'd say the thrust of the derogatory is to deride and undermine the culture of nicety, passivity, and 'let's just all get along'-ness, which is of course totally nauseating.
2. Describing a system of government based on the regulated balance of political struggle. "Fukuyama's 1992 essay 'The End of History?' argues that, with the defeat of communism, liberalism is the only viable political system and capitalism the only viable economic system, thus bringing an end to the history of political/economic struggle."
A self-regulating liberal system contrasts itself to a system of absolute ruling power (a monarch, dynasty, oligarchy, etc) in which political struggles take place as feuds, assassinations, schisms, and so on. In other words, the form of government that liberalism claims itself against is like a game of king of the hill, where only one person or group can be on top, and taking power means knocking the old power off the throne. The liberal political system encourages opponents to work together, or to fight each other within the system itself. We're familiar enough with some of the ways this is done: political parties, debates, elections, checks and balances, branches of government, bills of rights, protest, petition, lobbying, NGOs, and so on. A liberal government incorporates struggles as an engine for its own improvement and evolution. Many anarchists would point out that this is how the rule of a dynasty or religious line of accession becomes the rule of a class, and indeed that liberal government and capitalism go hand-in-hand.
Revolutionaries who want to take power, not work within the system to change it, are against liberal government. (Perhaps because liberalism is the bourgeoisie's form of government, and they are 'revolutionaries of the proletariat,' but also because revolution is a king-of-the-hill type of politics.) So lots of enemies of anarchy, politicians-in-hiding (leftists, by the way) are anti-liberalism, and have this in common with anarchists, which seems to be an area of confusion for some. (The-enemy-of-my-enemy-...-type thinking, I guess.)
In addition to the political definition, there is a social/philosophical one that supports or underlays governmental liberalism. This is the concept of the liberal subject. Liberalism relies on a certain definition of the subject as an individual possessed of rights which other subjects' actions may infringe on and for whose protection he consents to be governed (i.e. signs the social contract), provided that the government does its job as well as possible. (Incidentally, this is how and why anarchists disagree fundamentally with "anarcho"-capitalists, whose philosophy of the subject is thoroughly liberal). I'm pretty weak on this point; maybe someone else can flesh it out. I thought "Introduction to Civil War" did a good job on the subject.
To speak of leftism, rather than liberalism, my favorite definition is the one outlined in "Industrial Society and Its Future." I think FC does a pretty good job of getting outside of the left-right dichotomy by arguing that the entirety of modern society is leftist in that it is progressive and seeks to improve the system. Post-left anarchists have articulated a different critique of leftism, which is more in line with anarchist principles, but less sweeping and I think not effective enough in escaping political thinking in general.
(There is of course a third, liberal (definition #2), definition of liberalism: the opposite of conservative, the left-moderate-reformism of the Democratic Party and its foreign counterparts, a definition so irrelevant to anarchy that it is hardly worth mentioning, but does tend to get mixed up in things.)
