The directional vectors are one of the fundamental elements of physics and are an essential tool for learning mechanical concepts.
Vectors may be in 1, 2 or 3 dimensions having x, y, z respective components in different directions. The concept of vectors was born with curiosities of Aristotle and Newton. The need for vectors arose with past problems relating force and how should it be described, hence the concept of vectors was born.
The word vectors in physical term means something with magnitude and direction. Magnitude is the size measurement of a quantity that is represented by a positve number while direction can have many meanings. Consider, a car moving north-east along a road with an instantaneous speed of 20m/s, here the magnitude is the ';20m/s'; while the direction is ';north-east';. Now imagine a ship sailing at bearing of 030(degrees) with 10m/s speed, here the magnitude is ';10m/s'; and direction is ';030(degrees)';. Hence, magnitude may mean the size of the quantity but direction may vary according to a question or the information provided. Many vector problems in physics are answered by providing the angle from a fixed line, normally horizontal and mentioning whether it is above or below the line.
Vectors may be added and subtracted depending on the direction they are in. Vectors can also show whether a particle is in motion, the direction of motions or simply if it is in an equilibrium position (magnitude = 0, and stationary movement). Scalar and vector products can also help in understanding the concept and how vectors can be used in advanced mechanics to help understand the magnitude of the force coming out from a torque.
The following video may help in understanding the vector concept even more:
A bonus video on scalar and vector products (watch if you are interested in the phenomenon: