As others say - Private Browsing is a protection for your workstation/laptop - great if you want to clean it because it's used publicly. Not great for eluding your network admins.
The company you work for does have the right to set a policy for how it's resources are used, and monitor that employees stick within the policy. The analogy of a phone system is apt - you've reset your "phone", you haven't erased your phone bill which shows every number you called.
Depending on configuration, your company can see what IP addresses you visited, what URLs you requested, the traffic sent between the sites and you, content transmitted between the sites and you, and get a rough sense of for how long you were visiting the sites. The sites you visit do represent a security risk, and the company has a right to monitor and protect itself from that risk.
Practically speaking, it's rare for a company to scrutinize employee by employee. Collecting the data, sorting it for each employee, and going through it in details is just way more work than a company of any size wants to consider. In a big company, it's like finding a needle in a haystack, in small companies, the one guy who can do this is just too busy.
Generally, you have to do some or all of the following for this to come into play:
- do very poorly in job performance - to the point where they wonder what you are doing, because it clearly isn't work...
- have a major security issue - if you get hacked or get a virus, they will fix it, research why it happened and try to prevent it in the future. That extra scrutiny can bring on questions of why you were on a social site if the company policy prohibits it.
- visit sites excessively, and compromise availability of resources - if you are streaming Hulu, Netflix, YouTube, etc for the entire work day, you are limiting bandwidth for legitimate use. When the executive says "why is this so slow?", you don't want to be the reason.
In all honesty, I find the best answer to be - if you want your behavior to stay private, don't do it at work. The computer for work was given to you for work. Generally some polite social browsing in limited scope is not against the rules, if it doesn't impact your work... but the point of the computer they gave you wasn't for your personal enjoyment. If your privacy is important, do it at home, or pack a personal device with net access - it's getting easier and easier with smart phones and tablets to get off the company network entirely.