Magnetic field
A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials (such as iron) and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges (electric currents) such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field varies with location. As such, it is an example of a vector field.
Nonelectrostatic electric fields
To understand the origin, let us consider a wire loop, placed in magnetic field. According to Faraday's law of induction, if the magnetic flux is changed through the loop, an emf will be induced in this. The magnetic flux may be changed by changing the area of the loop or by changing the magnetic field. Why a changing magnetic field produces current in the loop? The loop contains electrons, which don't feel magnetic field, but if the magnetic field changes, they feel it. It is customary to think that if in a given region magnetic field changes with time, an electric field is induced in this region, which causes motion of electrons in the loop. But, an electric field can be there even if we don't place a loop. So, the complete discussion will be that if the magnetic field is changing, the electric field will appear, circulating the changing magnetic field.