A wire transfer involves moving money electronically.
The major advantage of a wire transfer is speed. The money arrives in hours and is immediately available. Contrast that with depositing a check in your bank. You will not usually be able to write checks against those funds for three days. If one were to mail the check, delays can be even longer. Who earns interest on the funds until they are credited to your account? What happens if the check is lost in the mail? (Someone stops payment on the first check--for a fee, and reissues a new check. But it's delay, delay, delay.)
Wire transfers also work well for international transfers.
Your bank, broker, or mutual fund company will usually be able to arrange a wire transfer if you request it. Some charge a fee for this service. You will want to consider if the fee is worth it. For major transactions involving large sums such as the sale of real estate, wire transfer is highly recommended.