What is the name of this statistical principal I was wondering how I could shorten this explanation into fewer words.  I am assuming their is a statistics term for this but I do not know it.  Is there one? 

If I flip a coin 10 times and get 8 heads I might not be surprised, however if I flip it 1,000 times and get 800 heads I should be surprised.

 A: @AndreNicholas gives two examples of principles that suggest your long run average for the  number of heads should stabilize.
For your specific case of flipping (I am assuming fair) coins, we also know that the mean and variance of this process are finite. In this case, we can further quantify your level of "surprise" using the Central Limit Theorem (CLT):
Let $H_n$ be the number of heads in $n$ tosses of a fair coin. Then the CLT states that:
$$2\sqrt{n}(H_n/n - 1/2) \xrightarrow{d} \mathcal{N}(0,1)$$
Therefore, for each $n$, we can quantify how "surprised" we should be at getting a certain number of heads using the normal distribution and the "standardized" number of heads (basically, mean number of heads minus expected fraction of heads then divided by standard deviation of the sample mean).
This relationship generally gets more accurate as $n\to \infty$.
So, you now have three principles to choose from. However, I've seen your particular statement/example mentioned in textbooks with regards to the laws of large numbers -- even though, technically, we the laws of large numbers do not provide warrant for being surprised by the results of any finite number of tosses.
