The volt is a unit of electric potential. It is fundamentally energy per unit charge (joules per coulomb). When we measure a voltage with a voltmeter it reads the electric potential difference between two points. This is the amount of energy in joules that one coulomb of electric charge would acquire if it moved from the point of higher potential to lower potential under the action of the electrostatic coulomb force.
A good way to think about this is to use the idea of gravitational potential which (close to the earth's surface) is proportional to height. A point at the top of a hill is at a higher potential (gravitational voltage as it were) than a lower point. Some mass e.g. water can naturally flow from high potential to low potential. It would be a CURRENT of mass. Similarly charge flowing from high potential to low constitutes an electric current. It is a flow rate of charge in coulombs per sec or gallons per minute in plumbing. The coulomb per second is called an ampere.
High currents do not necessarily mean high speeds of the charges themselves. In typical wiring the average "drift rate" of charge for DC is less than one inch per second.
