A solenoid is a length of wire wound into a "helix" or a coil. When in this configuration, the magnetic field INSIDE the coil is very strong and the magnetic field OUTSIDE the coil is very weak, nearly zero. Also, for a STRAIGHT solenoid, the magnetic field is independent of where you are inside the solenoid (how far from the axis) :

B = (mu naught)(n) (i)

where n = turns per length of the solenoid.
This equation is only for a straight solenoid. If you bend it into an arc or into a complete "donut", called a "torroid", the magnetic field is NOT uniform inside but depends on how close you are to the inner or outer edge. (See your textbook, pg 699)

The solenoid has practical applications in such things as mechanical relays, like the Bendix device that operates the starter on your car. The magnetic field of a solenoid showed up very nicely when I sprinkled iron filings on a transparent, loosely wound solenoid through which I passed 20 Amperes of current. Because it is loosely wound and short, there is some magnetic field outside the solenoid. The magnetic field is zero outside a long, tightly would solenoid only.