Hi,
If we consider a copper microstrip patch, the material is high conductive and therefore has loosely bound electrons. So what happens is that when a certain voltage is supplied to this patch, the electrons will travel around and this flow is the electric current. The electrons produces electric field around it and when this electrons are moving/accelerated (speed of light) due to the voltage, the field will be disturbed and will try to realign itself around the electrons the same manner when the electron is not moving. So the movement of electrons/charges will eventually produce radiation. The effect of current in the patch is radiation. As changing electric fields produces changing magnetic fields, the results will be electromagnetic radiation.
Substrates in microstrip patches influences the radiation pattern and also the bandwidth. The Er value of the substrate if its lower, the antenna will be able to radiate more efficiently. If the value is too high, the fields in the substrate will be tightly contained and therefore it affects the radiation.