A current source is a voltage source which - in ideal circumstances - creates as much voltage as needed for the specified current to flow. Think of it as a power supply with an adjustable voltage and a fairy watching the current and adjusting the voltage rapidly to preserve the constant current.

An ideal current source would suppply the required voltage in any case, so one with open terminals would output millions of Volts to create an arc through the air - of course this very rarely happens with real current sources.

A current source is not a single circuit element, but a close enough approximation can be made out of ordinary circuit elements. Such current sources are often used to drive LEDs and lasers where little differences in the voltage would lead to dim or burnt-out LEDs, but a current limiting resistor dissipating half the power would also not be acceptable.

Current sources also can be thought of as an opposite of ideal batteries, a.k.a. voltage sources. An ideal voltage source keeps the voltage constant across its terminals; a current source keeps the current constant across its terminals. 

Voltage sources "like" their terminals open - no current flows then, no energy is output. They "hate" being short-circuited - that results in infinite current and molten wires at the least.

On the contrary, current sources "like" their terminals shorted. Then only a tiny voltage is required to drive the specified current. But they "hate" being left open; they put out enormous voltages to try to push the current through.