This article is from the Magic: The Gathering Rules FAQ, by Patrik Linell (email@example.com) with numerous contributions by others.
No. Repeat after me: Mana is not the same thing as lands. This is
the biggest difference between Starter and grown-up Magic, and has proved
to be one that causes the most confusion. In Starter, lands are simply
tapped to pay for spells. In Magic, however, lands are tapped to add mana
to the player's mana pool. It usually stays there for a moment. After that,
the mana is taken from that pool to pay for spells or other mana costs.
Also, lands do not necessarily produce mana (though most do) and many of
them do other things as well.
Basically, your mana pool can be thought of as a bowl containing your
money. The points of mana (coins) in the pool aren't represented by
anything physical, because there's not usually many of them, and they
aren't around for very long.
So, as an example, Dark Ritual is an instant spell that adds BBB (that's
3 black mana) to your pool when it resolves, just as if you'd tapped 3
swamps. Afterwards, you can take that mana out of your pool and use it to
cast black spells.