To understand non-allelic genes, you must understand what is meant by alleles.
Let's say for a certain character (e.g. eye Color) you have a gene called the same Gene position now as the person called locus or locii.
Now we have two Genes that show the same character as eye color, but another color like one shows brown eyes and one shows green eyes, there genes will be denoted as Eb and Eg respectively. These genes are called alleles of each other. In other words, an alternative form of the Gene.
These genes are allelic genes. Now, if there is no Gene aligned to a similar focus for a particular character, it will be called a non-allelic gene. In other words, it can be said that genes that do not show any major characters may be considered as non-allelic genes.
I hope the concept is pretty clear. If not, please answer so that I will give some other example.