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A control is a duplicate setup of the experiment you are performing with everything identical except for the variable that you are testing.

Or, it is how the experiment would happen naturally, without you doing anything.

For example, if you are testing the effects of a certain medication on humans, you give half of the subjects the medication and the other half a placebo, which is a sugar pill that has no effect. The latter group is the "control group". Their purpose is to remove the psychological effect of taking the medication from the results of the experiment, so that the only variable remaining is the actual effects of the medication.

Constants are things that are kept the same for all trials, like making sure that every subject is taking a pill (and that they believe it is the medication in question, ever if it is only a placebo)

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