The term "mRNA" stands for "messenger RNA." This is usually enough of a hint to remember their function; to carry messages in the body, specifically messages for creating proteins.
The mRNA is like a rough copy of the DNA. The cell doesn't want to let the DNA leave the nucleus, not only because it would be too difficult to let it out one chunk at a time, but because this would subject it to damage and corruption. The DNA prefers to be inside the nucleus so that it can maintain high fidelity (faithfulness to its original code). The mRNA is a copy of the DNA that can be taken out of the nucleus and moved through the cell to reach the ribosomes, where the mRNA instructions can be used to actually make proteins.
You could make an argument for mRNA being responsible for making proteins, since they contain the instructions for the type of protein that's being made, but this job is more specifically performed by the ribosome, which would be a better answer. The other options are more relevant to DNA and DNA replication.