Coding standards, or coding conventions, are, in essence, sets of rules or guidelines designed to govern the process of code production in a software project, based on industry best practices, and, as such, they have been around for almost as long as programming itself. They are often applicable to a specific programming language, library, framework or environment, but they can also be language-independent, focusing mostly on style.
While coding standards can be somewhat informal, defined by a small team or corporation for internal use, most adopted standards aim to provide a formal definition of their rules, the reasoning behind each rule, and whether (and how) compliance with those rules may be verified. The main advantage of adopting coding standards, regardless of the formality and reasoning of a standard, is to have consistency across a code base.
In practice, to a programmer, complying with coding standards means restricting oneself to a subset of the programming language's features or syntax rules, in virtue of consistency, robustness and code readability. This tends to result in increased team productivity and reduced maintenance and production costs.
Here is a short description of programming style from Wikipedia:
Programming style is a set of rules or guidelines used when writing the source code for a computer program.