What generates variation in a species?
After mutations, which probably is the source of most variation.  The classic biological model of variation comes from accidents of history and environment. 

Many mutations disappear over time because they aren't helpful (advantageous).  The reasons variations persist for more than a few generations is that our differences have helped us to live successful lives and (in biological terms of success) have offspring.  In europe the lactate dehydrogenase gene and others like it that help people digest milk is active through adult life as the result of domestication of milk producing animals,  in asia, this trait is rarer or non existent as agriculture does not produce milk there (in most cases). 

This is a broad difference, but its true in smaller ways for all of our individual traits, or so the theory goes.  Individual family traits are helpful to create stronger family bonds, so even something like distinctive dimples or foreheads have claim to being an advantageous trait.  Its possible that blonde hair is the product of such an advantage - its a strong signal to paternity if the father is blonde for instance. 

Another answer to your question I think, is that there are probably mechanisms in the cell or in mate selection that increase or decrease variation in the community at given times of stress.  For instance, snakes are among the animals who have a particular ability to select gender depending upon the conditions the female is experiencing.  more males may increase variation in the community - fewer males and more females will decrease it.  (not by a lot mind you, but a bit). 

Additional response added as requested:

I see what you are getting at - why do children seem like such individual and unique things sometimes?

In sexual reproduction, the offspring are the product of the shuffling of the parent's genomes through meiosis, where the pairs of chromosomes we have are combined to make a single chromosome that will be half of the children genome.  

This process can result in completely novel combinations of genes while conveying many likenesses from the parent.  I would guesstimate that this is the major cause of the uniqueness of offspring/children.  

Also in mammals there are some cell lines which splice families of genes which will cause offspring to be potentially quite different from either parent.  Immune genes for instance are created from scratch from a bunch of genes that the parents give.  Making each offspring unique but also the product of the parent's genetic repertoire.  This can be significant as it affects health and also to some extent attraction - studies have shown that people who smell attractive to us are immunologically distinct from us.  

@David mentions epigenetic variation, which is a more recent significant development.  During our life, the germline (sperm/egg) DNA may be chemically labelled depending upon environmental conditions we experience.  A famous example is experiencing famine conditions, which caused the children to be born on the small side amongst other effects.   More recent studies have shown that this is a widespread mechanism to control cells in our body during our lifetime as well as communicate to our offspring how life is.  It is expected that this labeling does not affect us forever - the epigenetic labels change over the course of a generation quite often (we believe).