First, a quick primer on pH. pH is a chemistry term that indicates the acidity or alkalinity of a substance on a scale of 0 to 14, roughly. 0 is the most acidic, 7 is neutral, and 14 is most alkaline. So, something like a lemon juice concentrate, with a pH of 2, is acidic. Soap, with a pH of 8 would be alkaline. Pure water is a neutral 7.
The natural pH of skin is around 5.6-- mildly acidic. Intricate mechanisms in the skin create what is known as the acid mantle. Lipids and other trace liquids within the skin create this mantle, the acidity of which helps to defend the skin and body from pathogens (bacteria, viruses, etc).
The marketing concept of "pH balanced" products started with detergent manufacturers. All true soaps are naturally alkaline. When the pH of a soap becomes acidic, it turns in to a mushy slime and no longer works as a soap. Synthetic detergents, however, don't typically have this problem, so formulators are able to add acidifying agents to the formula to give it a mildly acidic pH that matches that of skin. So, marketers took this opportunity to tell you that because our skin is mildly acidic, our cleansers should be too. But, the truth is, just because something is "pH balanced" doesn't mean the product will necessarily be the best for your skin. For instance, cocamidopropyl betaine, a common "gentle cleanser" was named by the American Contact Dermatitis Society as 2004's "Skin Irritant of the Year" because it contains traces of a processing chemical called dimethylaminopropylamine that is highly irritating to skin. While a product with this ingredient may be "pH balanced" it can also cause some extreme reactions. Other potentially irritating ingredients in detergent-based "pH balanced" products are artificial colors, micas, "fragrance," and preservatives. "pH balanced" really is just a marketing term, and doesn't necessarily mean safety for your skin.
Because it is acidic, the most effective way to clean skin, along with excess oils, dirt and bacteria, is to use an alkaline substance--like a true natural soap. While it does remove the acid mantle temporarily, your most people's skin begins re-secreting the mantle immediately. This varies slightly person to person, and there are rare cases of this mechanism failing due to impaired skin function or illness. If you find that even the most mild soap is "drying" to your skin, it's likely a function of pH, and following up your soap use with a hydrosol (which are naturally mildly acidic) or diluted apple cider vinegar with re-acidify your skin and get rid of the tight or dry feeling. If you have troubles using soaps, you may also want to look at your water, as hardness can create soap scum that can irritate skin in some individuals.
Of course, not all soaps are created equal. I've used soaps that made my skin feel extremely tight afterwards, and others that are completely fine. And pH isn't necessarily related. You can have a soap with a pH of 9 that feels better on your skin than a soap with a pH of 7. It's about the concentration of the alkalinity (which is separate from the pH) and the amounts of free fatty acids in the formula, AND the presence or absence of other irritants (micas, fragrance, allergens, etc). Mildness doesn't necessarily correlate with pH.
Now, that's not to say that all detergents are bad, either. For instance the glucoside family of detergents (which we use in products that soap doesn't work, bubble baths and salt scrubs) contain no processing impurities and are also non-irritating to skin (I've used decyl glucoside at full strength on my skin with no issue.) pH adjustment can help, but it's all about overall formulation--percentages of surfactants used, humectants like glycerin, moisturizing oils and the presence (or absence) of common irritants.