Static Binary analysis is essentially the analysis of executable binary programs without having access to source code and without the need to actually run the program.
Early binary analysis methods consisted of simple pattern matching rules for know potential vulnerable conditions, such as calls to strcpy() or sprintf().
These methods are easily implemented with IDA scripts and even simple regular expression matching but as these simple vulnerable conditions became more and more apparent to now more security minded programmers this left only more obscure and complex vulnerabilities in software.