That's the part I don't get, why is the amino acid released?
Because that is their biological job, I suppose there are chemical reactions occurring that make the amino acid 'release'.
tRNA aka "Transfer RNA" have an amino acid on them, amino acids are the monomers of proteins (the building block). The tRNAs are looking for their matching bases on the mRNA. When they match up, they will drop off the amino acid they are carrying.
The amino acids form a polypeptide chain and then that will form a protein. And tadah, we have our protein (hence why this whole process is called production of polypeptides/proteins).
From what I've gathered, the mRNA is like a recipe or set of instructions, and the tRNA carry the ingredients (by putting them in the right order in the polypeptide chain).
Does this make sense (anyone feel free to correct me)? I strongly advise looking at some videos on this process, because this is probably one of the hardest processes in HSC biology and videos make it easier (to visualise what's happening).