Answer: Traits vary because of recessive and dominant traits
Explanation: When an offspring inherits traits, it receives traits from both its parents. For example, we can use the gene for brown or green eyes.
Brown is a dominant trait (meaning organisms only need one of its genes in order to have brown eyes) and green is a recessive trait (meaning organisms must have two green eye genes in order to inherit green eyes).
We can make BB be brown eyes with two brown eye genes, Bb be brown eyes with one brown eye gene and one green eye gene, and bb be green eyes with two green eye genes.
Say both parents have Bb, and the offspring can inherit one gene from each parent. The possibilities for the offspring gene would be BB, Bb, and bb. Therefore demonstrating how it is possible for an offspring to have different traits than their parents or siblings (a sibling could inherit bb and another BB, so one is green-eyed and the other brown-eyed.)
Obviously in reality there are many more factors that play into genes and much more diversity, however, this method pretty much explains the Punnet square method.