This article is from the Charmed FAQ, by Colin A. McGregor (firstname.lastname@example.org) with numerous contributions by others.
In the first episode we meet the three adult Halliwell sisters (Prue,
Piper and Phoebe) reunited at the old family home in San Francisco six
months after the death of their grandmother. Grandmother raised the
sisters after their mother died when Phoebe (the youngest) was very young.
Just after being reunited, the door to the attic in the home previously
always locked, unlocks. Inside the attic the sisters find a book titled
"The Book of Shadows", written by several generations of their ancestors
with various magic spells, and notes about various evil beings. The
sisters discover that they are the Charmed ones, good witches with the job
of defending the innocent and stopping various sorts of evil. In all of
this the sisters discover each of them now has magic powers. Prue has
telekinesis (the ability to move things by though), Piper has the ability
to appear to stop time in an area for everyone except good witches, and
Phoebe has the ability to see the future. In addition shortly into the
first season the three sisters discover they can all see and talk to
ghosts. The sisters are limited in that they can not use their powers for
their own personal gain (for example, no picking winning lottery numbers,
as Phoebe finds out the hard way).
This is not a static show, the characters do change, the sister's powers
do (very slowly) increase both in ability and scope. We also discover that
some of the powers are a little more complex than they first appear (like
Piper's seeming time stopping ability). Good and evil characters will show
up for a number of episodes and then leave.
In first season we see police inspector Andy Trudeau (and his assistant
Daryl Morris) become increasingly suspicious about how his sometimes
girlfriend Prue Halliwell seems to have a connection with many of his odd
cases which makes for a regular subplot. In season 2 there is a shift
caused by the death of Andy Trudeau and the presence of new neighbors Dan
and Jenny. In season 3 a further shift with the departure of Dan (and
Jenny) plus the presence of Assistant District Attorney Cole Turner. With
season 4 we have the death of Prue and a new (half) sister.