Circuits can require AC and DC at the same time to work. DC is electricity at a frequency of 0 Hz, and frequencies can be separated to do different things. An example is the LNB in the middle of a satellite dish. It is powered by DC from the receiver, while the high frequency AC signal to the receiver travels down the same wire, in the opposite direction.
It's quite common to have transformers that have a rectified output, but no smoothing. Often that is full-wave rectified so the voltage dips to zero each half-cycle, so 100 times per second with 50 Hz mains. It can be half-wave rectified where there is no output for half the time.
EIther way, there is an average voltage, the DC component, and an AC component, at either 100 Hz or 50Hz, superimposed on the DC.
It appears that something in the fan requires both an AC component and a DC component to make it work. I can think of a number of ways that could be achieved, but I can't work out why it has ended up like that. If you've got any photos or other information about the fan and the transformer it is meant to work with, that could help. Can you use and oscilloscope to measure the output of the transformer, preferably when the fan is running?