A conductor (wire) carrying an electrical current has a magnetic field around it. Even a long straight wire has a field, but if it is coiled up into a small space, the field is concentrated in that space. If another wire is coiled up and placed close to the first one, the two coils will share the field. Changes in current in one coil or physical movement of either coil will be felt by the other coil. Two coils close together have what is called "mutual inductance". It's like a mutual admiration society.
Inductance and Induction
Inductance is a term that indicates how much of a field will be produced, and induction is the process of transferring power from one coil to another.
By analogy, think about a piano string that is struck and is vibrating. If another piano is close by, the same corresponding string will vibrate too. The second piano string vibrates due to mechanical forces set up as compressed and rarified air waves produced by the first, so it is not quite the same thing as mutual inductance.
The value of inductance is determined by the size of the wire, length of wire, how tightly it is coiled up, and if it is coiled around a ferrous core. Inductance is one factor that determines the impedance of a cable.
Induction is a familiar electrical principle that we see every day. The big transformers on utility poles use induction. A power distribution transformer has an input coil (the primary) wrapped around a ferrous core and one or more output coils. (Secondary coils) When power is applied to the primary it generates a field in the core that "induces" power in the secondary. The voltage and current available at the secondary may be higher or lower than the primary depending on how the transformer is designed.