The Purpose of Fasting

We are commanded to “afflict our souls” on the Day of
Atonement. Does this really mean that we must fast for 24 hours? And if so, do
we fast by just abstaining from solid food during that time, or do we also have
to abstain from liquids? What are some of the reasons and purposes for
fasting? On the other hand, what are some of the motives which we should not
have when we fast? Does fasting have rewards? Can we fast in vain? And what is
the connection between reconciliation or at-one-ment and fasting?