Saudi Arabia feels threatened by Iran. Saudi is mainly Sunni Muslim while Iran is mainly Shi'ite Muslim. These two sects are at war with each other, especially since the removal of the Sunni government in Iraq by the USA and hangers on.
Iran is halfway to getting an atom bomb already. Possession of nuclear weapons by Iran would threaten the current Hegemon of the area, Israel. Saudi Arabia also has reasonable fears and wants to be on an equal footing with Iran, so they want a civilian nuclear program so that they can hide, or pretend to hide, a weapons development program underneath it. In this way they hope to prevent Iran becoming the hegemon, a hope they share with Israel.
Why SA is so late: SA is run by an small elite of a few thousand members of the Saud family who have gotten most of the oil wealth. These guys have, until now, had no interest in educating the masses for fear of revolution and have habitually imported technical expertise rather than face the hazard of educating their own people and then getting strung up by them. So that's one reason. Another might be that they, SA, provided a number of people who flew aircraft into the twin towers. Why would the USA, their greatest "friend", help the Saud family get started with Nukes and then see them deposed and replaced by hard-core Sunni fanatics?
Why don't the Sauds get the technology elsewhere? They might. Pakistan did, Libya did. But to do so would definitely sour their relationship with Uncle Sam and Israel.