Why is it important for the nucleus of a cell to make a copy of itself before mitosis takes place?

Cell division is a process that allows life to continue from generation to generation. It produces new cells for growth and repair. In order for this to occur, the genetic material of the parent cell, or its DNA, must be replicated so that it can be distributed to two daughter cells at the end of mitotic division. The DNA in an organism has hundreds or even thousands of genes. These dictate the production of proteins which can be structural parts of the organism, enzymes important in metabolic processes, hormones, or other important molecules. 

Therefore, a dividing cell replicates its DNA and passes a complete set of its genetic information to opposite poles of a dividing cell. These will split into two daughter cells.

In prokaryotic cells, the organism's genome (all of its genetic information) is found in a single long circular DNA molecule in an area called the nucleoid. Prokaryotic cells lack a nucleus. In eukaryotic cells, the genome is found in all of its DNA molecules distributed in the number of chromosomes for that species. These are located in the nucleus.

The processes of replication and subsequent cell division result in a complete set of the DNA distributed to each daughter cell. The amount of DNA found in body cells is called the diploid amount, which is the species number for that type of organism. Humans have 46 chromosomes in somatic cells, or body cells. The only cells which are an exception and have the haploid amount are called gametes, or sex cells, and these are produced by meiosis, a reduction division that only occurs in gametes resulting in cells with half the chromosomes as the parent cell. For humans, this amount is 23 chromosomes.

To conclude, mitosis is the division of the nucleus, followed by division of the cytoplasm into two daughter cells, in addition to some intermediate steps. The results of this process is that a single cell makes two genetically identical daughter cells which can be used for growth and repair. 

The asexual reproduction of single-celled eukaryotes such as amoebas is carried out by mitosis and binary fission. Prokaryotes reproduce by binary fission after the DNA in its chromosome is replicated. They lack a nucleus, however.

I have included a link showing how mitosis is part of the cell cycle. The link has a chart showing mitosis and its resulting daughter cells. It also shows meiosis as a comparison.