How does data travel inside a wire?

How does this current carry the data?

Current and voltage are inseperable. The current is flowing because there is a voltage on the wire, and there is a conductive path from that voltage to a lower voltage.

So we can say the data is encoded as voltage pulses or current pulses, it doesn't really matter. Often a high voltage (5 V) indicates a "1" and a low voltage (0 V) indicates a "0". But you could choose any two voltages you like. 3.3 and 0 V. 0 and 3.3 V. -0.8 and -1.2 V. According to what works best in your design.

I read somewhere that wires transmit data almost at the speed of light. How? What is carrying my data? Only EM waves travel this fast.

Another way to look at things is that the voltage at a location on the wire is just a simpler way of looking at the fact that there is an electric field between the wire and everything around it.

When a signal propagates along a wire, it's actually the electromagnetic field between the wire and a nearby "ground" or "return" conductor that is propagating. So it is actually an EM wave, not a massive object (like an electron) that is carrying the signal along the wire.

I read somewhere that wires transmit data almost at the speed of light. How? What is carrying my data? Only EM waves travel this fast.

Ohms law is great. It tells you that if you put 1 volt across a 1 ohm resistor, then 1 amp will flow. However it hides a darker truth that is best uncovered if you imagine that the 1 ohm resistor is several miles distant from the 1 volt source and connected by cable.

So, you apply 1 volt and some time later you will see that 1 volt across the 1 ohm load - well that's what you think might happen but it's more complex than that in the microseconds it takes to get down the cable.

In reality, the cable "informs" the 1 volt power source that it's taking 20 mA (this is for cable with 50 ohm characteristic impedance i.e. a lot of coax cables have this impedance). Clearly 1 volt / 50 ohm = 20 mA. So current is initially determined not by the load (too far away) but by the medium of the cable.

So, the 20 mA AND the 1 volt go hurtling down the cable as an EM wave - the cable ensures this and, there is an E field and a H field just like a real radio wave transmitted into the air/atmosphere/vacuum/medium. A vacuum has a characteristic impedance too - it's approximately 377 ohms; meaning that the ratio of E field to H field is 377.

The E and H fields journey to the far end of the cable to be greeted with a 1 ohm load and then strange things start to happen. If the load at the far end was 50 ohms it would be "end of story" but, because the load doesn't match the EM wave "characteristics" you get a reflection sent back to the power source and, after many times too-ing and fro-ing eventually the right current is sent down the cable to suit the load. It's all over in a few microseconds though.

So, it is an EM wave travelling down the cable. And, for that reason, it is always a good idea to consider the use of matching impedances to prevent reflections causing data corruptions.