When current flows through a battery or the secondary of a transformer, its receives power. Each charge leaves the battery with more energy than it had when it arrived. Since the energy of each charge has increased, the voltage (energy per charge) of the current has increased. Thus the current passing through the battery experiences a rise in voltage or a “voltage rise”.
Resistance is the measure of how much an object impedes the flow of electricity. The higher an object’s resistance, the less current will flow through it when you expose it to a particular voltage drop. To use the water analogy, resistance resembles a constriction in a pipe. The narrower the pipe (higher the resistance), the harder it is to push water through that pipe. If you keep the water pressure constant (constant voltage drop) as you narrow the pipes (increase the resistance), then less water will flow (the current will drop).
Current is the measure of how many charges are flowing through a wire each second. A 1-ampere current involves the movement of 1 Coulomb of charge (6,250,000,000,000,000,000 elementary charges) per second. Voltage is the measure of how much energy each charge has. A 1-volt charge carries 1 Joule of energy per Coulomb of charge. To use water in a pipe as an analogy, current measures the amount of water flowing through the pipe and voltage measures the pressure (or energy per liter) of that water.