mRNA is made off of one of the DNA strands in the nucleus. Note that the nuclear membrane has large holes.... and through them goes the mRNA out of the nucleus. The messenger then goes to the protein producing parts of the cell, that may include the endoplasmic reticulum and the ribosomes (themselves a type of RNA). Awaiting the mRNA are also transfer RNAs with attached amino acids. Then the "dance" occurs and the final product is a protein.
Apparently, it is not efficient to have protein production right next to the DNA, and it is more efficient to produce a number of mRNAs as blueprints so one can increase the production of specific proteins (like in cells of the endocrine system or digestive system).
