RNA is important to a eukaryotic cell because is plays a role in protein synthesis.
Protein synthesis begins with the transcription of mRNA from DNA within the nucleus of the cell. The mRNA then exits the cell via a nuclear pore and enters the cytoplasm of the cell. Every three nucleotides of an mRNA are called a codon because they code for a specific amino acid that is brought to the mRNA by a tRNA. The tRNA know where to place its attached amino acid because the tRNA has a complementary anticodon (also consisting of 3 amino acids). Ribosomes (containing rRNA) serve as the scaffold that joins the mRNA and tRNA together. The ribosomes move down the mRNA (this is called translation) so additional codons and anticodons can meet. Polypeptide bonds form as additional amino acids are brought over. Eventually, a stop codon is reached, signaling that no more amino acids are needed for that particular protein strand. The completed protein is then either used by the cell or packaged and exported.