Voltage is the cause and current is the effect. Once a source sets up a potential difference across a conductor, the free charges in it start to move, and the measure of that movement is the current. It is one of the two quantities a meter reads directly and one of the two that every circuit law is written in, so a clear definition earns its keep. Current answers a simple question: how much charge flows past a point each second.
The definition
Pick any cross-section of a wire and count the charge that crosses it. The current is the rate of that crossing:
the charge that passes in a time , divided by the time. Its unit is the ampere, symbol A, and one ampere is one coulomb per second. A current of 2 A means two coulombs, more than ten billion billion electrons, stream past every second. The ampere is one of the base units from which the rest of the electrical units are built, which is a historical accident worth noting: current, being the easiest thing to measure with a force between two wires, was made fundamental, and the coulomb was then defined as an ampere-second rather than the other way around.
Current has a direction, and here the convention set two lessons ago returns to bite. Conventional current is defined as the direction positive charge would move, from high potential to low, from the plus terminal of a battery around the circuit to the minus. In a metal the actual carriers are electrons, which move the opposite way, but every equation in this course uses the conventional direction, and the two only need to be reconciled when the physics of the metal itself is in question. For solving circuits, current flows from plus to minus through the external circuit, and that is all that is needed.
Drift is slow, the signal is fast
A surprise lurks in how fast the charges actually move. Inside a metal the free electrons are already flying about at enormous speeds in random directions, but with no field their motion averages to nothing. Switch on a field and a slow, steady bias is added to the chaos, a drift velocity that is astonishingly small: in a typical wire carrying a normal current, the electrons drift along at well under a millimetre per second, slower than a snail. Yet a lamp lights the instant its switch is thrown, metres of wire away. The resolution is that the wire is already full of charge everywhere, so the field, which travels through the wire at nearly the speed of light, starts all of them moving almost at once. Pushing the near end of a pipe already full of water makes water leave the far end immediately, though no single drop crossed the pipe. The electrons crawl; the push that marshals them races. It is the push, not the crawl, that lights the lamp.
Example. A current of 0.5 A flows through a wire for 2 minutes. How much charge passes, and roughly how many electrons is that?
The time is 120 s, so C. Dividing by the electron charge, electrons. A modest current for two minutes moves a number of electrons with twenty zeros after it, which is why charge is tracked in coulombs and not by counting.
Now you. A phone charger delivers 1.2 A for 90 minutes. How many coulombs of charge does it move?
Answer
C.
Current is the same all the way along
A single unbranched path carries the same current at every point along it, and the reason is conservation of charge from the first lesson. Charge is never created or lost in a wire, so whatever flows into one end of a resistor in a series chain flows out the other end and on into the next component, unchanged. This sounds obvious and is constantly forgotten. A resistor does not use up current; it uses up voltage, dropping the charge to a lower potential while passing every coulomb through. The lamp at the end of a chain draws exactly the current that left the battery, not some remainder. Where a wire branches, the current splits, and where branches rejoin, it adds back, in such a way that as much flows out of any junction as flows in. That balance at a junction is one of the two laws that solve every circuit, met in full a few lessons on, and it is nothing more than the statement that charge does not pile up or vanish.
Measuring it, and the danger of the ammeter
Because current is a flow through a point, the instrument that reads it, an ammeter, must be placed in the path so that the current it measures runs through it, in series with the component of interest. This is the opposite of the voltmeter of the last lesson, which is placed across a component to read the potential difference between its ends. The distinction is a common beginner's trap with a costly failure mode. An ammeter is built to have almost no resistance, so that inserting it barely disturbs the circuit, which means connecting one directly across a battery, as a voltmeter would be connected, offers the battery a near short circuit through the meter and can destroy it. Current is measured through, voltage across, and the two are not interchangeable. With charge, voltage and current now defined, the stage is set for the single relation that ties current to voltage in most materials, and the property that stands between them, which is resistance.