Suppose there are 100 genes that "cause" height.
Each gene has the same small (1%) effect as the others.
Say each gene has two alleles, one of which makes height a bit taller,
the other makes height a bit shorter;
call these alleles + and -.
Say each allele is equally likely to occur.
Each person is a random mix of + and - alleles.
Person A: the alleles for the genes from 1 to 100:
+-+++++--+-+---+-+--+--+----+------+---+--+--+-+-++-+++---+-+++++--+-++-+-+-++-+-++++-+-++---+---+--Person B:
-+++-+--++---+-+++------+-+-+----+++----+++++---+---+-++-+--++++++-++-++-+---++++-++++-+++--+++-+-+-A has 46 +'s and 54 -'s, so will be a bit shorter than average person.
Say 1000 people (to get a good sample size).
Count the frequency of each number of +'s. Graph these counts in a histogram: normal distribution!
Most people are near the average, that's "normal". Fewer and fewer people are shorter and shorter or taller and taller than average.
A normal distribution arises whatever the proportion of +'s is.
For example, if the + allele is likely to occur 80% of the time:
two people's 100 height genes might be:
++++++++-+++-++--++-+++++-++--++++-++++-++++++++++-++++++++++++--++-+-++++++-+-+++--++-+++++---+-+-+ 75 +'s -++++-++-++++++++++++++-++-+++++++-+-++-+++++-++++++++-+++-++-++++-++++--+++++++++++++++++--+++++-+- 81 +'sA thousand such "genomes" could look like this:
