For example, want to find all messages from a particular client? Just type the first few letters of his or her e-mail address in the Search field. Immediately you'll see matching results; click the right one to immediately filter your inbox accordingly.
The new feature also simplifies "operator" searches. For example, to run a document search, type "doc" and then click has documents. Search Autocomplete will immediately paste in the full operator for said search: filename:(pdf OR doc OR xls OR ppt) OR docs.google.com OR spreadsheets.google.com. Then you just type your actual search parameters and you're off to the races.
Good stuff, Google! Keep the Gmail goodies coming.