One of the most important things on a guitar which can change the sound and completely affect the tone and signal power sent to your effects and amp is the pickup. Basically, the pickup is designed to take the acoustic vibrations from the strings, and convert the waves into electrical signals. Usually, they do this by using fine wire coiled around a bar magnet. In the same way that an electromagnet can create motion from electrical energy, it can also do the reverse. The movement in the air from the vibrations of the strings reaches the pickup, which changes the movement in the air into an electrical signal, and then passes it on to your effects pedal chain. See the video below:
Passive pickups are usually the most common pickups found in electric guitars, and they use the coil and magnet method described above to convert kinetic energy to electrical energy, which can pass through the circuitry and components of effects pedals like distortion, overdrive and such. These pickups are not particularly strong, as they are not backed up by any power source. Different tones are achieved largely from the position of the pickup in relation to the guitar body. A pickup closer to the neck and fingerboard will provide a deeper, warmer tone, while the same pickup placed closer to the bridge of the guitar will produce a more treble dominated tone.
On top of this, passive guitar pickups usually come in two different styles, the single coil which is common on Stratocaster-type guitars, and the hum bucker (two single coils acting together) which is favored in models like the Les Paul and SG. Hum bucking pickups are more powerful, as well as being a lot harsher tone-wise, and so they are often preferred for rock music. They make use of phase cancellation to drastically reduce the hum common to single coil passive pickups, and usually sound great when driving a distortion pedal in your effects rig.
Active pickups do not rely on the same coil and magnet method as passive pickups; instead they require an additional power source – most commonly a 9V battery – in order to change the vibrations into electrical signals. They have the advantage of being extremely low noise when compared to their passive cousins (which are often affected by things in the external environment such as lighting).
Active pickups are often shipped as a standard feature in guitars intended and designed for heavier music like metal and hard rock, because they send a much stronger signal to your effects rig, and therefore drive overdrives and tube amplifiers more easily into overdrive and even distortion.
They often contain active EQ controls, which means that a guitar designed for use with active pickups will give the player much more control over the tone, even before it is sent on to effects pedals.