The big things I remember from that era is that the iPhone was the first phone with an unlimited data plan which Apple/Jobs beat AT&T into submission to get. Until then you had to worry about every last byte you used on the dinky carrier-grade apps and the lousy WAP websites.
This worry removed, and the fact you actually had a real browser that could open real websites were the two main features that to me seemed like a huge leap forward.
Its also clear that the carrier wasn't ready for it. People with the original iPhone would get entire boxes mailed to them for their Cingular statement, itemizing every data transaction, but then all flat rate charged.
I had an original iPhone and did not get such statements. As I recall while Cingular was indeed not ready to handle unlimited data for customers, it wasn’t really a problem for the first iPhone since it wasn’t 3g. Once the 3g dropped , it was a problem since people were actually able to consume a large amount of data.
This worry removed, and the fact you actually had a real browser that could open real websites were the two main features that to me seemed like a huge leap forward.