I'll take a stab at a non-math based explanation.
Think about what a transformer is, I'm going to use a single phase simple AC core and coil transformer we all use every day. If you took one apart to sell for scrap, you would find it is essentially just two long pieces of wire wrapped in a coil around a piece of steel. How it transforms from one voltage to another is based upon the phenomenon called "induction" which says that if you move a magnetic field across a conductor, it causes current to flow in the conductor. So the transformer, in it's steady state, creates electro-magnetic fields that form around one coil that permeate the steel and make it into a magnet. As the AC current rises and falls, the magnetic flux of the magnet is rising and falling too, so then creating current flow in the other wire coil, which is wrapped around the same steel core. That voltage will be lower or higher than the original one by the ratio of how many times the coils are wrapped around that magnet in relation to each other, called the "turns ratio".
But that is at the STEADY state, and at some point, you must START this process. If you look at the circuit, other than the fact that it is coiled, the wire is just a wire; it is in essence a "short circuit". Once the magnetic fields are created and begin interacting with each other, the current flow in both sides "impedes" the flow of current in the other through a process called "mutual induction". In works kind of like this: Coil A has current flowing, that creates magnetic flux in the steel, which induces current to flow in coil B, which ALSO induces magnetism in the steel, which then opposes the flow of current in coil A, which limits the current in coil B etc. etc. etc. Everyone is happy.
But for a BRIEF moment, BEFORE the flow of current in coil A creates magnetic flux in the steel so that current in B can oppose it, there is NO impedance to the flow of current through coil A, it really IS a "short circuit" for that instant, where the current flow is slowed down ONLY by the natural resistance in the wire itself. The magnitude of that current, which can be anywhere from 1000-2000% of the steady state maximum current, is called the "magnetizing current". It only lasts as long as it takes for the steel to become magnetized and depending on the design, can range from anything between a few cycles (at 60Hz, a cycle is 16.7ms) and a minute, but most fall into that 1-3 cycle range.