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If all the needles, or a block of needles, were to be simultaneously selected, each would require its own actuator. It is much cheaper to select the needles at a single selection position in serial formation, using between one and six actuators, although the time interval between each selection impulse is shorter.

This sentences have been recited from Knitting Technology by David J Spencer. I think using between one and six actuators means first and sixth actuators are not used, rather second, third, fourth and fifth actuators are used.

Please say what it actually means.

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Let me take another example to try and explain :

David, come to my office between 10 and 11 tomorrow.

Now this means that the speaker wants 'David' to come to his office at any time between 10 and 11. David can go to his office at 10 or anytime after 10, but before 11. Ideally, the speaker doesn't want David to come to his office after 11. So by using 'between', the speaker is giving a window in which David can visit him in his office.

In your context, "between one and six actuators", simply implies that one actuator can be used or even six actuators can be used serially. Also, any number of actuators between one and six can also be used. So in simple terms,

...using between one and six actuators....

means using one, two three, four, five or even six actuators is all right.

PS: Mathematically speaking, this is a closed interval [1,6], where 1 and 6 can be used.

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