What gives rise to the normal distribution? I'd like to know if anyone has a generally friendly explanation of why the normal distribution is an attractor of so many observed behaviors in their eventuality. I have a degree in math if you want to get technical, but I'd like to be able to explain to my grandma as well

I'm not sure if this is good for your grandma, but I'll give it a try. 
Normal distribution here is meant to be the one symmetric around the mean (which is also the mode, most frequent observation), i.e. with 0 skewness.
Normal distribution arises as a limiting case of many other distributions with the increase of the size of the sample, e.g. Binomial or Poisson due to Central Limit theorem (hence limit) when you standardize this distribution around the mean, $Z=\frac{X- \mu}{\sigma}$ (hence central). In essence, people noticed that different unrelated distributions have a very similar convergence pattern if you standardize them in this way.
It also arises naturally in many aspects of real life, since many phenomena have some tendency to symmetry around the mean. For example (I think it was one of Fisher's works) if you look at  all people with weight=$m$ and rank them in the order of increasing heights, the frequency of heights forst increases, reaches a peak and then decreases, so if you look at the histogram of heights, it resembles (as the sample size keeps growing) a bell-shaped structure. Same can be said about many other processes/phenomena. Their frequency first grows, then peaks around the mean, then reduces.
So people decided to give it a name, Normal distribution.
