Will formatting a drive erase it?

It depends on
kind of format. There are two types of format that you can perform.

A "quick
format" will simply erase the part of the drive that shows where all of
the files are located on the drive. The data is still on the rest of the drive
though. One can use programs such as R-Studio that recognize different file systems and can detect files
and directory structures on the disk. This means that you, or others, can still
recover the data.

A low level
format writes 0's to the entire disk (and this can take a long time). This
prevents software tools such as R-studio from reading the data on the drive.
However, professional data recovery companies and data forensics personnel can
still recover the data. This
is because the 1's and 0's on a disk are stored magnetically. However, the bits
are not considered to be a 1 if they are 100% magnetically charged in one way
or a 0 if they are 100% magnetically charged in the other way. Instead, the
drive uses a threshold--a bit is considered a 1 if the magnetic strength is
above a certain point or a 0 if it is below it. Because of this, professionals,
using special devices, can determine what a bit's previous value was, before it
was changed to its current value. In fact, they can do this to see the bit's
history for several of the previous times the bit was written.

When you do a format from within windows, it normally
writes 0's to that particular partition and then sets up a blank file table
that shows where the files are located on that partition.

If you truly
want to destroy all data on the disk beyond recovery, use a program such as Eraser.
It has several different algorithms to write pseudo-random data to the disk to
destroy the data. The different methods provided different levels of security
against the ability to recover data by rewriting the bits on the drive with
random data a different number of times (ranging from 1 to 35 times, depending
on the algorithm). Take note:
Because you are writing data to the entire drive (in some cases, multiple
times), this process can be time consuming.

If you plan on
selling a pc or a hard drive, I strongly recommend you do a low level format or
use a tool such as Eraser to destroy the data beyond the recovery methods
available to the average person.