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The number of turns of wire directly relate to the strength of the magnetic field.

Since the magnetic field is created by moving electrons we could argue that the more electrons are moving, the stronger the magnetic field would be.  A given length of wire contains a certain number of electrons.  Twice that length will contain twice as many electrons.  If a solenoid is made with more "turns" or "wraps" of wire, then it must create a stronger magnetic field.

3 turn solenoid 6 turn solenoid
This solenoid has only three turns or wraps of wire around it.  Its magnetic field is not very strong. This solenoid has 6 turns of wire around it.  If all else is constant, the magnetic field should be twice as strong since it has twice as many turns.
In conclusion we could say that the number of turns of wire around a solenoid is directly related to the magnetic field strength of the solenoid.

In reality it is not quite direct, since doubling the amount of wire would increase the resistance.  The increased resistance would lead to less current from the same source.  This animation ignores this effect. 
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