XQuery is a functional programming language used to query XML documents. It is based on XPath, which is a language used to address parts of an XML document. XQuery was developed by the World Wide Web Consortium (W3C) to be a more expressive and flexible way of working with XML data.

XQuery has a rich syntax that allows for complex queries to be constructed easily. Queries can be written to retrieve specific data, filter results, or aggregate data across multiple documents. The language is also designed to be extensible, with support for user-defined functions and types.

Syntax of XQuery:
The basic syntax of an XQuery statement includes a prolog, a main expression, and an optional order-by clause. The prolog defines the namespaces used in the query and any user-defined functions or variables.

For example, consider the following XQuery statement:

```
declare namespace html = "http://www.w3.org/1999/xhtml";
let $doc := doc("books.xml")
for $book in $doc//book
where $book/genre = "Mystery"
order by $book/title
return <li>{$book/title}</li>
```

This XQuery statement retrieves the titles of all books in the "Mystery" genre from an XML document called "books.xml" and orders them alphabetically. The resulting output is a list of book titles wrapped in HTML list items.

Best Applications of XQuery:
XQuery has many applications in various fields like data management, web services, and scientific research. It is particularly useful in cases where data is stored in XML format, such as in scientific databases, web services, or content management systems.

Some of the best applications of XQuery include:

1. Web Services: XQuery can be used to extract data from web services and combine it with data from other sources. It is commonly used in enterprise service buses to transform and route data between systems.

2. Data Management: XQuery is useful in managing and querying XML databases. It can be used to extract and transform data, and to generate reports and visualizations.

3. Scientific Research: XQuery is often used in scientific research to analyze and manipulate large datasets. It is particularly useful in cases where data is stored in XML format, such as in genomics, bioinformatics, and other scientific databases.

In conclusion, XQuery is a powerful language for querying and manipulating XML data. Its rich syntax and extensibility make it a popular choice for many applications. By understanding the basics of XQuery syntax and best practices, users can leverage its capabilities to extract and transform data in a variety of fields.