How does regression analysis help one understand how the typical value of the dependent variable change? 
regression analysis helps one understand how the typical value of the dependent variable changes...
   -- http://en.wikipedia.org/wiki/Regression_analysis

What does this mean? What "typical value" is it talking about? What kind of change is it looking for? Positive or negative or what? Change in what? Percentage? I'm confused. 
Lessons learnt:
* greened answer is good in that it had concrete clearness
* wikipedia documents a ton of info, most of which are unreadable and unusable
* most (80%) ppl, while im sure good meaning, just dont know how to give good answers
* and only human... have so many flaws, and thereby closes good questions  
 A: Say you wanted to guess someone's weight, but you only know their height. How could you do this?
If you had access to measurements of the the height and weight of many people you could draw up a graph with height and weight on the axes and put dots at the points of each pair of measurements. What you will see is a general trend for taller people to be heavier, but there is a lot of scatter around this trend.
Regression is the process of using some technique to estimate the typical relationship between the height and weight. So, after doing the regression analysis you might be able to say 
Typically, someone who is 1.8 metres tall weights about 80Kg, but someone 2
metres tall weighs around 100Kg.

Of course plenty of people who are 1.8 metres tall weigh more or less than 80Kg, but your analysis might tell you that in the absence of any other information your best guess for their weight is 80Kg. The regression analysis tells you how this typical value for weight changes with height i.e. taller people are typically heavier.
Regression is not limited to one variable predicting another, for instance what if we also knew the biological sex of each person? After doing some regression analysis we might be able to say
Males that are 1.8 metres tall typically weigh around 85Kg but Females
weigh around 75Kg.

Note that I just made up all these numbers. The actually numbers would depend on doing some regression analysis on a real data set (which I haven't done for this quick explanation).
A: Let's assume, for the sake of simplicity, that you have a dataset with a variable that is normally distributed.  For example, you might have data on the heights of American males aged 20-29.  Someone might ask you, 'how tall is the typical twenty-something guy?'  What would you answer?  You would probably answer with the mean value of the distribution (5'10").  This is the best candidate for the typical value in several senses of the word, and of the distribution of heights.  
Now let's say that someone asks you, 'how does the typical height of an American 25 year old vary based on the height of his father, when his father was 25?'  For every possible height that fathers have, there will be a corresponding distribution (also presumably normal) of heights of their sons.  These are conditional distributions.  They can be characterized by their means as well (and standard deviations, but we'll leave that out for the moment).  Assuming you had data on the fathers' heights at 25 as well, a regression analysis can help you understand how the means of these conditional distributions are varying as a function of the father's height.  Note that the change could be positive or negative; it just tells you how the conditional mean changes as fathers' heights change.  
