Because in Welsh we have different forms of the verb "Bod" depending on if the sentence is positive, negative or a question. This is most easily shown using the formal forms. So "Rydw i " is a positive sentence (I am). "Dydw i ddim" (I am not) is a negative sentence, and "ydw i" marks a questionof "I am". Now the for the third person singular it's slightly less regular. "Mae" is the positive form, "Dydy/Dyw" is the negative form and "Ydy/Yw" is the question form. (The course teaches the colloquial forms so don't worry if you haven't seen "Rydw" before.)
Is "Dyw" a dialect form for "dydy"? Also, only auxiliary Welsh verbs change in the negative or question form? So we have "Maen nhw ddim hoffi yr pili-pala" - We do not like the butterfly, but "Dyn nhw ddim yr pili-pala" - "We are not the butterfly" (sorry for weird sentences as there were not any basic vocabulary yet). Also I read that in literaly Welsh verbs are conjugated as in English/French etc.
Yes "dyw" and "dydy" are dialect forms of one another, "dyw" being more southern and "dydy" northern. In any negative sentence with bod it must be the negative form so "dydyn/dydan nhw ddim yn hoffi pili-pala pala" although often these days this becomes "dyn/dan nhw ddim". Also note "y pili-pala" not "yr pili-pala". Yes most verbs can be conjugated but this is not just an aspect of literary Welsh as in we still do it today, you should learn about this later in the course.