Sulphates are, as Sherrie said, very strong detergents. And cheap. That is why they are present in most hair and skin cleansing products. They foam well, they are strong, and they are cheap.
There's really nothing WRONG with using Sulphate products. The bottom line is, they will dry your hair and skin more and be more harsh than other cleansers.
After using a strong detergent on your hair or skin for a long time, the natural oils in your skin and your scalp will over-compensate. In the long run, you'll become a bit dependent upon the strong detergents because your skin and scalp will seem oilier and oilier. If you were to take a break from the detergents and use milder products for a few weeks, your natural oil/sebum balances will resume.
Although I wear hair extensions and sell them, my main goal has always been to grow my own hair long- as quickly and healthily as possible. I use a specific washing and conditioning routine (while wearing or not wearing extensions) and have been doing so for about 6 months now. I wash my hair every other day. I do a wash day of CO (conditioner only wash), then three wash days of CWC (condition wash condition), then I do a clarifying wash with Apple Cider Vinegar (the ACV clarifying is especially important when I wear the adhesive tapes/Protac/Protapes/Supertape--- it cleanses underneath the tapes very well and reduces the sogginess). Then I begin the routine again. None of the products I use contain Sulphates- I personally find them very drying to my own hair and my hair extensions. After I stopped using Sulphate products I noticed my extensions did last much longer, and my own hair was much less dry.
At first I did not feel my hair was getting that clean with the CO and CWC washes- but once my natural hair/scalp oils returned to a healthy balance, I find those washes to be very cleansing and the condition of my hair has improved tenfold.
I know this whole routine is a little extreme for most people (I also quit using all heat styling tools in May. I though my hair looked like #^$% at first, but, again, after a period of time it resumed a natural luster, shine and texture that I am very happy with). Like I said- my goal is to grow my own hair long. But- my main point is just that the Sulphates ARE very strong and ARE , by nature, a very drying substance.