Valid HTML conforms with standards as described by the World Wide Web Consortium (also known as the W3C -- http://www.w3.org/). The W3C defines these standards so software from different vendors will understand HTML in the same way.
It's similar to having a dictionary and grammar rules for English.
Validation is the process of verifying (with software) that the HTML conforms to all the rules of the language. Like most languages, HTML is evolving, so there are versions (and dialects, like XHTML).
Validation is like spell-checking and grammar-checking your HTML.