Baby shampoos usually use "surfactants" or wetting agents rather than soap - which is what most adult shampoos use as a cleansing agent. Johnson and Johnson shampoos use 4 different surfacants - Cocamidopropyl Betaine, PEG-80 Sorbitan Laurate, Sodium Trideceth Sulfate, and PEG-150 Distearate. These are less harsh than normal detergents, but still perform in cleaning as it basically makes water more effective. (Adult shampoos usually use Sodium Lauryl Sulfate and Sodium Laureth Sulfate - soap based detergents.)
Water will still cause tears depending on its pH levels, so the claim that it is a "no more tears" formula is a bit misleading. Anyone might still tear up from the pH level, but surfactants do not cause any more adverse reaction than the water you are using to wash with. "As gentle to the eyes as pure water."
ETA: Baby Shampoo does NOT have any numbing agents. PET shampoos do, but not baby formulas. Here is the ingredient list from the website:
Water, Cocamidopropyl Betaine, PEG-80 Sorbitan Laurate, Sodium Trideceth Sulfate, PEG-150 Distearate, Fragrance, Polyquaternium-10, Tetrasodium EDTA, Quaternium-15, Citric Acid, Yellow 10 and Orange 4. May also contain: Citric Acid, Sodium Hydroxide.
(This product does NOT contain either Sodium Lauryl Sulfate or Sodium Laureth Sulfate as some answers would have you believe. Sodium Trideceth Sulfate is a milder surfactant commonly used in baby shampoos.)