For immunization, you body must recognize the virus and thus be able to start an immune response. For this, the body needs characteristics of the virus. In the case of the coronavirus, these are the spikes (hence the name of the virus). Therefore, the construction plan of the spikes was found out and converted into a recipe (the mRNA) for the body.
During the vaccination, the prescription reaches the body and cells well protected. The recipe can be read and processed here. The ribosomes read out the mRNA and the t-RNA brings amino acids in the right order. The spike in the body is then assembled from these building blocks. The produced spikes are harmless (the information from the virus is missing) but the body can learn to identify the virus with the help of them.
The genome of the body is not changed. The mRNA is not incorporated anywhere and is itself not very stable and is rapidly broken down. A cake recipe does not change the function of the oven or kitchen appliances.