mRNA technology has been around for a while. What kept mRNA from being used in widespread vaccination was not having a way of protecting the mRNA long enough to get inside of cells and the ribosomes, where it can be "read" to construct a protein.
Instead of admitting this they (Moderna, Pfizer, etc.) went ahead with a lipid-soluble coating.
A lipid-soluble coating guarantees the injected mRNA to easily pass through cell membranes and get to the site of action (ribosomes). But it also meant that, unlike other vaccines, which have their particles taken up in normal lymph flow and end up in lymph-nodes, antigenic molecules are processed by dendritic cells and stay in the extracellular space (outside and in-between cells - the interstitium), otherwise the mRNA in these vaccines ends up everywhere, easily passing from the interstitium to the blood stream and across the blood-brain barrier.
Compared with getting a virus, the virus is only able to bond with and enter some cells; injecting its genetic material and taking over production to make more virus. It is limited to cells displaying molecules each virus is capable of binding to (in the case of SARS-CoV-2 this is a molecule called ACE2).
In "normal" vaccination only dendritic and a few other immune cells (which are designed to ingest and deal with antigenic molecules) end up with viral proteins in them. These specific cells are part of the immune reaction that ends up with long-term and robust immunity. With mRNA vaccination the injection is in the deltoid (most of the time) but the particles of mRNA move easily move in and out of cells and across biological membranes. Any cell, and subsequently its ribosomes, which come into contact with the exogenous mRNA, will start to produce the altered SARS-CoV-2 spike proteins that the mRNA instructs for.
In the normal course of cellular function the master copy of your build and operating instructions (DNA) has a chapter photocopied as needed (mRNA) and sent out to factories (ribosomes) which read the instructions and build proteins according to them. During this process, whatever protein is being made is reported back to the immune system. This happens by each of your cells taking one of the things its ribosomes are making and displaying them on the outside of their cell membrane.
Security (T-Cells of the immune system) come by, but can't get inside, they just look at the sign to see if something is off. If something is, they can nuke the whole city (induce lysis) or tag the sign for other bulldozer immune cells to come by and level it. This function fights both cancer and viral infection.
If either of those things cause a cell to start making abnormal or foreign proteins then the cell is instructed to kill itself (lysis) or it gets tagged to be destroyed by other immune cells.
Until recently you could only end up with antigenic (things which set off an immune response) molecules displayed to the immune system on subsets of cells. Either a virus infected your cells and that virus could only attach and enter a tiny number of overall cells in your body (like SARS-CoV-2 and cells which display ACE2), or you could get cancer (which is essentially one cell over and over and over).
Outside of that, antigenic molecules would be immediately destroyed by natural killer cells or would be collected through lymph to be processed and displayed by dendritic cells in lymph tissue (lymph nodes mostly). These dendritic cells look like massive tree root systems and all they do is process foreign material and display it on Major Histocompatibility Complex. That's the molecule complex that announces what's going on inside a cell to the outside world. It is the security (the immune system) that monitors to know if there is an issue inside, as security is a cell itself, and can't enter another cell.
The immune system is blind to the intracellular environment besides these signs (MHC). One type of T-Cell, T-Helper Cells, move up and down the "root system" of the dendritic cell, just looking at all the signs.
In this way, your lymph nodes and spleen (where this process mostly happens) act as security checkpoints, eventually coming across fragments of anything that ends up in your body. If they find something wrong, they induce an immune response to that thing which will eventually reach wherever the molecules they saw came from.
By injecting these lipid-soluble mRNA particles into peoples bodies; littering them throughout all tissue, dependent on each individuals weight, lipid percentage, hydration, cardiovascular state, anatomy, etc. Wherever concentrations of these end up you have random cells which will start to produce altered spike proteins.
The immune system notices this and starts attacking those areas. As each mRNA vaccinated cell is destroyed they spill their contents of altered spike protein (cytotoxic itself) into the local area.
The vaccine makers know the path to immune activation is through MHC (signs), and don't really address or care about all the excess spike proteins being made.
In the background, ribosomes are churning out actual spike protein into the inside of the cell. This is how viruses reproduce as well; once infected more viral particles are constructed inside a cell, but they don't get to release and go infect other cells until the infected cell is destroyed and they can escape.
All the atoms in your body are replaced about once a decade. Even your bones are constantly re-structured by osteoclasts and osteoblasts, so every 10 years you have entirely different atoms making up those bones. Even cells that generally don't replicate or die until you do, like neurons and muscle constantly replace their constituent parts.
The MHC displaying the product the ribosome are making will stay embedded in the cell wall until that section of the membrane is replaced due to other natural process (e.g. endocytosis).
This means that people who end up with persistent neurological or cardiac side effects may have them for years, until most of the signs stating the cell is making spike protein are torn down. For neurons in the brain, that could be years, not to mention the fact that in the mean time, the immune system is actively trying to kill off any of those cells, and often successfully.
There is so much we don't understand about this. A gigantic portion of your genome is dedicated to MHC. We don't have any idea about the mechanisms we are playing with. Not only are large swaths of MHC black boxes but the whole question of Clonal Selection (how your body 'knows' what is you and what isn't you, and therefore what to attack) is an open question.
There are no longitudinal studies on any of this, the safety data is non-existent beyond "it probably doesn't kill many of you in the first 90 days." It will take years to collect the data and produce irrefutable results, which is why the normal process is around 6 years from a working product. Without control groups, even that data will be easy to skew in interpretation though.
