However, you needn't fear. The article gets more and more detailed as you read on, so if you don't want to dig really deep into this, just stop reading when the questions you are interested in have been answered and things start getting boring. It is used to formally define the grammar of a language, so that there is no disagreement or ambiguity as to what is allowed and what is not. In fact, BNF is so unambiguous that there is a lot of mathemathical theory around these kinds of grammars, and one can actually mechanically construct a parser for a language given a BNF grammar for it. The most famous of these is YACC, but there are many more.
Alternatives usually consist of both symbols and something called terminals.
Terminals are simply pieces of the final string that are not symbols. Another variation on BNF grammars is to enclose terminals in quotes to distinguish them from symbols. So, the language described by a grammar is the set of all strings you can produce with the production rules. If a string cannot in any way be produced by using the rules the string is not allowed in the language. Valid sentences in the language described by this grammar are all numbers, possibly fractional, and possibly negative.