Why and how?
It may seem obvious to suggest that a parent facilitates its child's learning but it doesn't always happen, and it is vital that with so many after school activities the student is assisted in finding a regular time to fit their piano playing into their schedule. On top of this, as a solo instrument, playing at home can sometimes feel lonely and isolating for a very young learner, so having the encouragement and close proximity of a parent can be a positive support to their experience. The time at home is also the time when technical habits are learned and ingrained, so having an extra eye and ear keeps things on track.
Parental support doesn't have to make learning the piano seem like hard work. On the contrary, it can add a fun and interactive element to what can sometimes be a struggle in the early stages when there is so much new material to absorb and digest. Having a parent help schedule the time, and gently discipline the child to keep to this schedule, can be an enormous benefit when there are so many other distractions.
Music is an expressive and communicative art so a student needs to feel comfortable with themselves, and allowing them an inquisitive mind and lively ear, and the freedom to translate their expressions to sounds, is vital in their growth as musicians. It is challenging but necessary to encourage them without judgement so that they feel free to explore the colours and sounds of the instrument without feeling censored, but are guided in areas where there is a 'right' or 'wrong' (ie note).
Finally, I'm a great fan of rewards, but when extra motivation is needed make sure the rewards are for trying rather than for getting it 'right'. Sometimes the road to getting things right is rather long so boosts along the way can give us the encouragement we need to continue to the end.