Monitoring and measuring the impact of social media is a vital step in any social marketing campaign.
Essentially, there are two question that you need answers to: 1.
Is your social media working? 2.
Are you measuring your social media efforts to know that it is working? Measuring is critical, I get that.
But what do I measure? That's the question that prospects put to me all of the time when they ask me why their campaign isn't working as planned.
My response is that it is important that the things you measure not be subjective and that they are measured regularly (yeah, I know, we are back to that pesky consistency thing again).
With that, here are some things that I would focus on:

• Visitors and sources of traffic - Easy enough to do through Google analytics or site stats.
  But this can be revealing to tell you where your message is getting out to.
  
• Network size in terms of followers, fans, members, etc - This is the area that Dennis explained to you that can be easily measured.
  Don't get caught up in the size vs quality issue.
  You need both.
  But if I had to choose one, I go for size.
  
• Quantity of commentary about your brand or product - This is an indication of if you are truly engaging your readers or they are just saying "Great post" to get a backlink.
  
• Sentiment or quality of commentary about your brand or product - Are people raving about your product or service? If they aren't, then what are you doing about it?
• Search engine ranking position - In many ways, things such as Page Rank is an indication of how serious the outside world perceives you.
  Besides, no one has deep enough pockets to drive all of their traffic to their site using Pay Per Click (PPC)
• Leads generated - Are people approaching you to learn more about your product or service, asking for a quote, etc as a result of your engagement.
  
• Progress toward achieving your social media objectives - We have talked about plans before.
  You have to have one.
  Are your efforts succeeding? How so? In what way? (Be honest with yourself here!)
• Engagement with influential bloggers, journalists, Twitterers, etc - Are you getting asked to be quoted in your newspaper for what you do? Are other people on the web taking notice of your product or service? Maybe you need to set a goal to engage with someone who is much larger than the pond you hang out in?
• Sales conversions or other ROI metrics - At the end of the day, most organizations gauge their success from these numbers.
  It is down on my list, but at some point, it HAS to fit into the equation.
  
• Competitive share of social media coverage for your niche - Does it bug you when people/products are talked about in your niche and that you aren't part of the conversation? The question to ask yourself is do you have anything to contribute?
• Criteria to identify and profile audiences - Are you reaching the folks that want or need your product or service.
  Above, I indicated that I would go larger numbers over targeted numbers.
  That is true, but like the sales conversions, there has to be some element of reaching your target audience if you want to be successful.
  

I am not saying that this list is all inclusive.
I will say that this list encompasses the measurements made by most successful/influential businesses marketing good/services.
Do you need to measure them all? If you have the time and inclination, these metrics will probably give you the E-Myth approach of being able to work on and not in your business.
What I would suggest is to start with 2 or 3 of the above and gradually add in others.
That being said, you should be measuring! And now you know the things to measure as well.