It's available and powered by the CirrusSearch (based on ElasticSearch) which is the used search engine in the MediaWiki sites, and the Wikimedia platform.
Some usage examples:
Note: Full guide reference, and source - on Wikipedia: Help:Searching#Search_string_syntax.
As for your question:
Logical operators
The search engine supports boolean logic in searches. The logical operators include the "-" (minus sign) character for "logical not", the AND, the OR, and the grouping parentheses brackets: (_).
Logical OR must be spelled in capital letters; the AND operator is assumed for all terms (separated by spaces), but capital AND is equivalent.
More examples:
- Simple
AND, OR: "credit card" OR "payment card", "credit card" AND "payment card" - will work as expected.
- Suffixed tilde character for fuzzy search ("sounds like") - For example, searching for
charlie~ parker~ returns Charlie Parker, Charles Palmer, Charley Parks (up to two character difference, not including the first one).
- Wildcard search - searching
face*e - starts with face and ends with an e with anything in the middle.

Extra reading
Read more about the search engine and this extension to unveil their full functionality and features.