When a dc coil connected to a contactor or a solenoid is energized, it draws a high current. This high current is necessary to generate enough magnetism to pull the plunger or the contactor. This is known as the pull in current.
After the the contactor has been pulled in, less current will be sufficient to hold the coil. This is called the holding current.
Hence, to limit the current after the contactor has operated, a series resistance is connected. This is known as the economy resistor. The economy resistor enables the design of contactors which can draw heavy initial current and less holding current (resulting in lower power consumption during normal operation).
In the case of AC coils this is not required as the current is limited after the initial inrush due to the back-emf.