To "reduce your calorie intake" means to eat and drink fewer calories.
"Calories" are a measurement of the amount of energy food contains. You should be aware that what Americans call "calories" are actually kilocalories. So if someone says that a cookie "has 400 calories", that really means that it has 400 kilocalories, or 400,000 calories to be technical. Most Americans don't know the scientific definition of a "calorie", though.
To "reduce your intake" of something means to lessen the amount of something that you put into your body. This phrase is used when you're talking about the human body in a technical or scientific way.
"Calorie intake" is an example of using a noun (calorie) to modify another noun (intake). You could also use the adjective version of "calorie" instead:
You must reduce your caloric intake in order to lose weight.
This version seems more formal than the example given at top.