When a website is submitted for AdSense approval, it is firstly analysed by their algorithms and if it passes their algorithms clear, then the website gets approved in 2 to 3 days.
If it takes longer than 2 to 3 days, this means the website triggered something in their algorithms, to roll-over the website for manual human review, which can take upto a week, more than a week, upto a month or more than a month : Whatever goes into manual reviews for any product or service of Google, can take an unpredictable amount of time, as Google is usually under-staffed and infact they have been firing more employees lately.