Wavefront is the continuous locus of all the particles of a medium that are vibrating in the same phase. A light source sends out disturbance (waves) in all the directions.
In a homogeneous medium, the velocity of light waves is same everywhere. So the disturbances reach all such particles at the same time. These particles are at the same distance from the source and so they vibrate in phase with each other. The locus of all such particles is called wave front.
Spherical, cylindrical, plane and so on.
You must have noticed that in all the above diagrams the arrows representing the ray of light are perpendicular to the wavefront.