To be conservative with an estimate is to wish to avoid underestimating, while to be liberal is to want to avoid overestimating.
So, if you were in a position of giving an estimate, you look at the consequences of underestimating or overestimating. For example if you were an employee of a company, and your boss says "How long will it take you to do X?", you might think:
"If i underestimate the necessary time, i'm going to end up delivering it late, and look bad. On the other hand, if I overestimate the time my boss will probably just say "Ok" and put that in the planning schedule, then later I get to deliver it earlier than expected and look cool."
So, there's bad consequences for underestimating, and no bad consequences for overestimating. So, you would overestimate, and you would call that a conservative estimate.
If you were a freelancer, there's also potentially bad consequences for overestimating: they might give the job to someone cheaper. So, you need to balance the two potential problems. If you were really desperate for the work, and willing to take a risk on having to work nights or something, you might give a liberal estimate - a cheap one in this case.
So, logically, a conservative estimate is one where you deliberately overestimate the resources (time, money, materials etc), and a liberal estimate is one where you deliberately underestimate the resources (perhaps because you think it's going to be easy, and you want to make sure the client gives you the job).