Autosomal chromosomes are the 'normal' ones - you have 22 pairs of these.
You also have 1 pair of sex chromosomes - XX in your case, XY for your brother. So the YDNA is from this single Y chromosome. Unlike autosomal chromosomes it is passed directly from father to son without mixing with the mother's DNA. So it varies much less as you go up and down the ancestral chains, but can only be used to find male relatives.
MtDNA is mitochondrial DNA. This is from separate little 'organs' within the cell, not from the main cell nucleus where all the autosomal and sex chromosomes live. MtDNA is passed directly from mother to child (both sexes) without being mixed with the father's DNA. So like the Y DNA it changes much less with each generation.
Siblings don't have the same DNA as each other (unless they are identical twins) because, as a PP said, the half they inherit from each parent is is random.
As a simplified illustration, imagine you have 23 numbered bags, each containing 1 black ball and 1 white ball. Go along the line and pick a ball from each bag; then put them all back and do it again. Both times you will end up with 23 balls, but you won't have picked the same colour ball from each numbered bag both times. That is essentially what happens to form an egg, and to form a spermatozoon. (Actually it's more complicated, because new balls are made every time and genes are also mixed up as part of that process).
So the egg that you grew from contained a random half of your mother's autosomal DNA, a randomly selected one of her X chromosomes, and all her MtDNA.
The egg your brother grew from contained exactly the same MtDNA but a randomly selected half of the other types.
Same for sperm - each one has a random half your father's autosomal DNA. But no MtDNA, and we know you got different sex chromosomes.