What does "it's a liberal school" mean to you?

The one I know of is independent, although some state schools do have more liberal ethoses.

Independent but government funded so feels like a state school. Based in a grotty city.

Can I just ask whether any of these liberal schools are state, or are they all fee-paying?

I think liberal means different things to different people but overall I believe it is an environment that allows a lot of freedom. My son's school has no uniform - I wouldn't call that liberal. But it let's children dye their hair bright green, have Mohicans, piercings etc, and at break time, children have no boundaries as to where they can go within the school and what they can eat. Of course, if you don't practice music for a minimum length of time each day then they would chuck you out, so in that sense it's not liberal. Fwiw, about three pupils look a bit...different!

Also forgot to mention descusion based learning and guardian reading teachers!

To me it would be one where the school operates on trust, so few rules but bad behaviour is definitely punished and as a result isn't repeated. I wouldn't necessarily say no uniform, but I would include calling teachers by their first names. Also an unpressurised environment, where the children are able to speak their minds and express themselves. Strong infulence of arts in the school.
My DN goes to what I would class as a liberal school. They don't push their students but still get excellent exam results. The students are allowed into town at lunchtimes and the teachers operate on trust - if that trust is broken then you lose the privilage to go into town. They also have no uniform and call teachers by first names. Music, art and drama are compulsory until the end of year 9 and all year 7's do thinking skills. Ideally I would love my DCs to be in a shool like this.

my dc goes to 'a liberal school' which is also a highly selective school, so perhaps we are talking about the same school.
In terms of my dc's school, it means they leave the kids to their own devices as much as possible allowing them to make their own mistakes and learning from the consequences of these to act in a more mature way.
What this equates to is the minimum of school rules. The school opens early and kids can spend time in the morning unsupervised, I am not sure if this is the norm for most comps.
Another example is they might not apply the school uniform rules that stringently, so if you have your shirt hanging out or if you are not wearing a tie they will not give you a detention, they might not even say anything to you. If you are a girl and you roll your skirt up to your knickers, probably wouldnt get a comment. It is quite a good environment for a mature child who wants to be treated as an adult. Teachers treat the kids as grown ups.
If you have a child who benefits from a more disciplined environment then perhaps a liberal school may not be the right place.
In a lot of high performing comps, they have very stringent rules. A local high performing comp near me, makes the kids do a lot of exams early etc, but the liberal school does fewer gcses and all and only in year 11.
The end result of the liberal school is they try to create someone who thinks for themselves and is confident and self assured.
I am not certain but I think this comes through even within the teaching as a proportion of the lesson is discussion based, which can turn into a bit of a free for all.
Politically, more left wing as well, certainly in our case.