Much like any other software WordPress and the plugins you use must be kept updated security and performance reasons.
An outdated plugin makes your website vulnerable to attacks.
Not using the latest version of a plugin also means that you might be missing out on some features that could make life easier for you.
A website with a number of outdated plugins generally results in a slower website. That's frustrating for your users and Google may not like you very much.
It is also easier to get tech support on a website that has all its plugins updated and problems are easier to spot and fix.