Liberal has multiple definitions that get blurred together. It can mean:
1. A political ideology based on limited government, or at the very least weaker government. Implies a stronger individual.
2. A political ideology characterized by openness, tolerance, and greater freedom of action for the individual.
3. A political ideology characterized progressiveness, AKA wanting to move forward. As opposed to conservative (wanting the status quo), and reactionary (wanting to go back to the way things were before).
4. Leaning to the left politically, which is a huge bag of worms to define. Probably but not certainly involves some combination of the above 4. Might also contradict them too. Depends on what counts as moderate in wherever you live, and what the big talking points are.
5. Generically, characterized by openness or relaxed limitations. AKA, "a liberal sprinkle of sugar".
IN GENERAL, if you ask someone in the US they mean 3-4. 2 is usually included but that could be disputed depending on your view of the phrase "economic freedom". According to definition 1 (which is I believe a somewhat outdated view), both American parties use a liberal ideology since they both want limitations on the government but in different senses. Broadly speaking they also both agree with separation of power and all that.
An important point is that compared to other "western" nations, the American political spectrum is shifted right on most issues. Remember, Obamacare is considered left leaning here, but in most nations on Earth it would be considered right wing politics.