Lactic acid is an alpha hydroxy acid (AHA) extracted from milk. Despite such a natural origin, most forms used in cosmetics are synthetic because that form is easier to stabilize and formulate with, plus it's vegan.
In a pH-correct formula (ideally a pH between 3 and 4) and in concentrations between 5 and 12%, the lactic acid exfoliates on the skin's surface. It does this by breaking down the material that holds dead skin together so it can fall off naturally as it once did. Lactic acid also has moisturizing properties (like sodium lactate, it is part of the skin's natural moisturizing factor, or NMF).
In addition to these benefits, lactic acid strengthens the skin's barrier by encouraging it to make more ceramides, a key component of healthy skin. It also greatly affects the skin's microbiome and helps keep its first line of defense strong by positively interacting with a neuropeptide in the skin's surface known as Substance P, resulting in the rapid spread of signs that the skin is stressed.
Like glycolic acid (another popular AHA), it helps brighten an uneven, dull skin tone. https://www.paulaschoice.com/ingredient-dictionary/ingredient-lactic-acid.html?q=Lactic%20Acid&fdid=ingredients