Why are controls important when testing a hypothesis?

By having a control (which is subjected to the same conditions as the test subject[s] except for the condition or substance you are testing) you can eliminate other influences, by comparing the control to your test. In testing medication, for example, this is VERY important - if only to account for the PLACEBO EFFECT that occurs.

By having a variable, you can compare the results of a series of applications of the specific condition or substance you are testing, which should show at what level(s) the experiment works and possibly what side effects occur.

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The variable provides the data that are to be interpreted and compared.

The control provides a reference, or standard, for comparison. Without this reference, no valid comparison is possible so, the data is moot, and the hypothesis can't be tested.