It is intended to reduce redundancy of data.
For a more formal discussion, see the Wikipedia http://en.wikipedia.org/wiki/Database_normalization
I'll give a somewhat simplistic example.
Assume an organization's database that usually contains family members
id, name, address
214 Mr. Chris 123 Main St.
317 Mrs. Chris 123 Main St.
could be normalized as
id name familyID
214 Mr. Chris 27
317 Mrs. Chris 27
and a family table
ID, address
27 123 Main St.
Near-Complete normalization (BCNF) is usually not used in production, but is an intermediate step. Once you've put the database in BCNF, the next step is usually to De-normalize it in a logical way to speed up queries and reduce the complexity of certain common inserts. However, you can't do this well without properly normalizing it first.
The idea being that the redundant information is reduced to a single entry. This is particularly useful in fields like addresses, where Mr. Chris submits his address as Unit-7 123 Main St. and Mrs. Chris lists Suite-7 123 Main Street, which would show up in the original table as two distinct addresses.
Typically, the technique used is to find repeated elements, and isolate those fields into another table with unique ids and to replace the repeated elements with a primary key referencing the new table.
