What is so significant about electron spins and can electrons spin any directions? I just want to know what is so significant of with direction electron is spinning. Does it have any effect on the element or on the atom?
Also, does electron must spin up or down or can they also spin sideways or vertically?
 A: the direction of electron spin is of great significance. For example, to fit two electrons into a electron orbital surrounding an atom, their spins must be pointing in opposite directions. In this sense, electron spin is at least partly responsible for the structure of the periodic table and for the manner in which chemical elements react with one another.
A free electron zooming through space is free to have its spin vector pointing in any random direction, but if you use a magnetic field oriented in some particular direction to set up the electron for a spin measurement, you will detect that electron spinning in either one direction (spin vector aligned with the field) or another (spin vector aligned opposite the field direction)- no inbetween values are allowed.
A: Electron spin is proportional to the magnetic dipole moment produced by an electron that is not traveling.  This acts very much like the dipole moment of a current traveling through a circle of wire.  The magnitude of the spin vector is set, but it can be in any direction.
When you measure a component, any component, of that magnetic dipole moment, and thus the spin, you will get only one of two results.  It will be fully along that axis in one of the two possible opposite directions.  If you change to a perpendicular axis, you will still get only one of these two results but along the new axis.  To measure something, you must interact with it.  At the quantum level, making a measurement forces the object into one of the allowed states of what you are measuring.
