To find this out, let's look at the history of electricity.
From about 2750 BC, people have acknowledged the existence of an electrical current, but did not understand it. The journey of understanding started with Thales, was improved upon by Benjamin Franklin, and almost finished by Michael Faraday. During electricity's development, electric instruments were constantly being fabricated, and the growth of electricity reached its ultimate point by the 1830s. Everything was complete and all electric instruments were in common usage.
Until this period, current was understood to be due to the flow of a charged particle, but they did not know its charge. In fact, it was not even known that a different type of charge existed. Therefore, they assumed that the current was due to positive charges.
When J J Thompson discovered the electron in 1897, it rocked the whole world of physics, because it had a different type of charge which was opposite to the charge they had known. Also, its movement produced current and the movement of the electron was opposite to that of the known "positive charge" for current generation. After extensive research, it was found that the current was indeed due to the electrons and not these "positive charges."
This meant that the current direction they had always assumed was wrong, and that the real current, due to electrons, was in the opposite direction. However, they could not bring this change to the theory of practical electricity as all instruments were well understood and were accustomed to using the existing laws. Since the current direction did not pose any problems practically, despite the fact that electrical instruments were fabricated assuming the opposite direction, the change was not made.
But, to differentiate the current due to "positive charges" and the current due to electrons, the terms "conventional current" and "electric current" were introduced. The word conventional means, "conforming or adhering to accepted standards."
So, conventional current is the current due to "positive charges," and electric current is the current due to electrons.
Despite the direction of these two currents being opposite, there is no change in their magnitudes as they are actually the same current, just understood differently.