Vectors are quantities that have both a magnitude and a direction. A common example of a vector quantity is velocity of an object. Unlike speed, velocity is a vector quantity and needs both direction and magnitude for complete description.
Anything that has a direction can be resolved into its x and y components. For example, when we throw a ball, in a projectile motion, it makes some angle with the horizontal. Knowing that angle and magnitude of velocity, we can resolve the velocity into its x and y components. We can use the basic understanding of trigonometry to do that.
If the vector with a magnitude, M makes an angle of d degrees with the horizontal, the components of the vector can be calculated as:
Horizontal component = M cos d
Vertical component = M sin d
For example, a projectile thrown with a velocity of 10 m/s at an angle of 60 degrees to the horizontal, will have a horizontal component of
10 cos 60 = 5 m/s.
Hope this helps.