Why can be a question or a statement. If it is a question then it is signed like you would naturally think of the word why (touch your forehead with fingertips of the dominant hand and pull out to a y). However, when used as a statement it should be signed like reason (the sign for think or think with an R).
Question: “Why did you eat that?” That is a basic question and the word would be signed like normal.
Statement: “Helping others is why we are here.” Think about this statement like this: “Helping others is the purpose or reason we are here.”
Statement: “Do you know why we are here?” Here the word why is not used as a question (the question word is do). The word why is again used as a statement. This sentence could be signed: “Do you know the reason we are here?”
Many of the question words can also be used as statements. They have a different sign when used this way.