Quoting from Apple's security documentation for this release:
Multiple vulnerabilities existed in Java 1.6.0_45, the most serious of which may allow an untrusted Java applet to execute arbitrary code outside the Java sandbox. Visiting a web page containing a maliciously crafted untrusted Java applet may lead to arbitrary code execution with the privileges of the current user. These issues were addressed by updating to Java version 1.6.0_51. Further information is available via the Java website at http://www.oracle.com/technetwork/java/javase/releasenotes-136954.html
If you turn off Java in all your browsers and make absolutely sure you don't download and run any standalone Java apps, then the update probably isn't essential, but otherwise it is, since at least some exploits do exist in the wild; they're not just theoretical.