Transformers are used to take the "line" voltage which is the incoming power and change it to a lower voltage the pcboard and typically the mood lights can use.
Most common is the changing the voltage of either 120vac or 240vac to reducing the voltage to 12-18vac. In doing so, the transformers allow a standard pcboard to work. These boards are typically operated on 12-18vac. Some boards have so much demand that there may be a need for TWO voltages on the board. Usually one transformer is able to supply the step down voltage needed for the board to operate both.
If incoming voltage from the transformer goes above the board's need (higher than 18vac on most) that can damage the board's electronics. If the voltage goes below the board's needs it can either act poorly in operating the spa, damage the board, or just shut down.
So a properly in/out transformer voltage is critical for safe and reliable operation of the spa.
Best thing is transformers are very dependable. But power surges or use can cause them to fail. If the spa is not operating the tech will check the incoming power (from the house) and the drop down power from the transformer to assure the pcboard is getting proper voltage.
As a side use, the dropped down voltage from the transformer typically also powers moods lights and such if the spa has them. Older spas with a single clear light bulb likely uses a 12v bulb. Also most color LED mood lights also operate on 12vac.
In example to the left your see a FOUR wire socket to the pcboard. This socket is the transformer socket. This is the most common style.
You can't see in this picture but there are TWO yellow wires and one black/one white wire.
Typically the incoming power to the transformer is the white/black as shown. REAL CARE must be exercised in this test because you test with the spa's power on. If you aren't qualified to work with live currents its best to seek perfessional help.
The red probe in this example is touching the BLACK top of the connector. The black probe is touching the WHITE top.
You slide the probes to barely touch the copper top of the clip. You should have either 115vac or 230vac. If you DO NOT, there is an issue with incoming power. If you DO have correct power present then the transformer is receiving the right current.
SECOND part of the test (not shown) is do the same but the top YELLOW copper tops of the plug. You should have 12-18vac. If not then you know the issue is the transformer.
If you DO have 12-18vac on the transformer output then either the board's fuse has blown or the board itself is damaged.