Square brackets [] mean array. In your case of code:
public double[] MethodName(){ .... }
You have a public MethodName method that returns an array. The double indicates the type of array, i.e. Stores an array of double objects.
EDIT: Forgot to answer the return question. But for your line of code, MethodName returns an array of type double (which will depend on the implantation inside the method body). Hope this helps (I'm also new to Java, climbing the ladder of SO rep)
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