Question

why is oil so important to the
countries of the arabian peninsula?

Answer 1

Arabia produces much of the world's oil; in Saudi Arabia, oil profits are a large part if the economy. Check these sites for details.

https://www.cia.gov/library/publications/the-world-factbook/geos/sa.html#Econ

http://www.country-studies.com/saudi-arabia/oil-industry.html

Answer 2

i understand but other websites don't tell me a lot about WHY it is important.

Answer 3

Because it's there.

Because they have so much of it, and other countries (US included) consume so much. The higher the demand, the higher the prices that can be charged.