Conservative and liberal are political ideologies, or a set of views on politics.
It can be very confusing, seeing as each political ideologies have many different meanings, depending on the type of issue (social or fiscal/economic) or the time period which you are talking about. Liberal ideas of the 1800's would be considered libertarian today, while a mix of socialism and democracy would amply describe today's liberal views.
Generally when people say conservative in modern times, it usually describes people that are about keeping traditional and moral values in the social realm, while advocating lower taxes and spending in the fiscal/economic realm.
Generally when people say liberal in modern times, it usually describes people that are about relaxing standards and accepting different cultural or moral view points in the social realm, while advocating for a larger government role, more taxes and more government spending in order to achieve income equality while sacrificing freedom in the fiscal/economic realm.
Of course not all liberals agree on the main points of liberalism, nor do all conservatives agree on all the main points of conservatism.
Conservatives tend to be republicans, while liberals tend to be democrats. Of course there can be conservative democrats and liberal republicans though.
EDIT:
Party aside. If you are a person that strongly believes in economic freedom and low government spending, but believes in gay marriage and abortion rights. You would be considered a Fiscal conservative, but liberal on social issues. Or perhaps considered a libertarian.
And just the opposite to that scenario, you'd be a fiscal liberal, but a social conservative. Of course nothing is always black and white, and label never truly do justice to any one persons beliefs. It's just a generalized label.
So a republican, let's say, favors higher taxes and spending for welfare programs, but is very much opposed to abortion and gay marriage. One could label him a moderate republican, or a liberal republican. Either way, it all depends on the issue or type of issue you are categorizing them for, or where they sit (which way they lean) overall amongst all of their views. You first have to define the terms to understand the context fully.
