First of all: there is no requirement to associate your SE profile with your real life identity, it is a personal preference to do so or not.
The reasons to do that are also personal and diverse.
Some people thrive in anonymity (you don't even have to create an account to participatean account to participate on SE) as their questions, opinions and recommendations should speak for themselves. Q&A's need not be backed by a "real name" to be "more valid" or "better".
Your online personal interests, questions, opinions and recommendations may not always reflect well on current and potential/future customers/employers/spouses and/or friends. Hence a nick name on your profile rather than a real name.
Others might desire the opposite, they don't want anonymity and want to be personally recognised for their SE contributions.
An SE profile based on your real identity might be part of a larger online presence and can be used to support your social network, career, products and/or business.