I am a bit confused. During Meiosis, DNA is replicated to form a cell with half the DNA and likely to have variations. But since the replication process of meiosis and mitosis are the same, why do DNA in different cells of an individual organism not have variations? Or do they have variations that are just not expressed?
Think of Meiosis as a means of producing half the genetic material you (and your partner) need which, once combined, produces offspring that inherits genetic material from the both of you. Think of Mitosis as a means of producing a full, exact (as exact as possible anyway) copy of chromosomes during cell division =)
Meiosis - results in a cell with half the genetic material (haploid), which is later fused with a similar haploid cell from the opposite sex (gametes) to produce a single cell with a full set of chromosomes (diploid cell). I.e. a sperm and an egg (each haploid) which fuse to produce a zygote (diploid). Important to note that during Meiosis, there is cross over between chromosomes, so that you end up with genetically diverse gametes (i.e. each haploid cell is different to one another - part of the reason your kids don't all look exactly the same).
Mitosis - results in a cell with a full genetic copy of the cell it was replicated from. That zygote will replicate using mitosis again and again until the organism dies. During Mitosis the cell tries to preserve as much of it's integrity as possible, so there isn't cross over. But the process isn't perfect in humans - each division results in shorter telomeres, and a cells also accumulate mistakes that result in "bad code" being passed on - UV damage for example.
With regards to expression, there is the concept of epigenetics - you may inherit certain genes, which (through various mechanisms) will be "locked" and not expressed in yourself, but may be expressed in your children. You might notice that kids have characteristics of their grandparents which aren't present in their parents.