I'm a little confused about meiosis and gametes. Are the cells dividing to form offspring, or are they dividing to make a sperm and an egg which later make the offspring?

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In your body, normal (diploid) cells will have 2 of every kind of chromosome, in humans= 23 pairs or 46 chromosomes total.  To make offspring, each parent has to give only one of each kind of chromosome, so they do mEiosis to rEduce the number of chromosomes, creating gamEtes (spErm/Egg) with 23 chromosomes each.  The egg and sperm join thru fertilization, creating a new cell w/46 chromosomes called a zygote.  That zygote cell will do mItosis to make gazillions of Identical copies of itself, thus creating a new human.  Remember, 46 chromosomes is the diploid chromosome number for humans, other species will have their own number, but the principle is the same.  Meiosis reduces the number of chromosomes, diploid to haploid, usually done for sexual reproduction.  Mitosis makes identical cells to the original.