Cursors allow row-by-row prcessing of the resultsets.
Types of cursors: Static, Dynamic, Forward-only, Keyset-driven. See books online for more information.
Disadvantages of cursors: Each time you fetch a row from the cursor, it results in a network roundtrip, where as a normal SELECT query makes only one rowundtrip, however large the resultset is. Cursors are also costly because they require more resources and temporary storage (results in more IO operations). Furthere, there are restrictions on the SELECT statements that can be used with some types of cursors.
Most of the times, set based operations can be used instead of cursors.