Examples:
humans have 23 pairs of chromosomes so 23 X 2 =46. So this is 2n or diplioid (di means two, tri means 3)
egg and sperm have only one set of chromosomes, no pairs. This is 1n or haploid.
Non-disjunction means that one or more of chromosome pairs failed to separate during meiosis, so a gamete (egg or sperm) has an extra chromsome, or is missing a chromosome. The offspring, with the wrong number of chromosomes, is aneuploid. If it lives. As an example, the offspring can have 2n -1 (one missing), or 2n+1 (one extra). The case of humans having the wrong number of chromosomes usually results in the death of the fetus very early on.
Aneuploidy example (2n +1):
Trisomy 21. The person has an extra member of the chromosome set number 21. Probably due to non-disjunction.
https://en.wikipedia.org/wiki/Down_syndrome - the main risk factor for this condition is the age of mother.
Think of it this way. The female fetus (inside mother) at age ~4 months, the ovaries undergo the first phase of meiosis. Before birth. So the fetus becomes an adult. No problem so far. But. If she decides, at age 41, to have children things are not great. Meiosis has continued (oogenesis, creating a viable egg for each mentrual cycle). At this point, meiosis II proceeds after more than a 41 year break. Meiosis is more likely to go wrong after such a long time, resulting in aneuploidy.