Though its long name does not reveal it, this polymer molecule (big molecule from repeated subunits or monomers) is a relative to the super common, water-loving thickener, Carbomer. Both of them are big molecules that contain acrylic acid units, but Acrylates/C10-30 Alkyl Acrylate Crosspolymer also contains some other monomers that are hydrophobic, i.e. water-hating.
This means that our molecule is part water- and part oil-loving, so it not only works as a thickener but also as an emulsion stabilizer. It is very common in gel-type formulas that also contain an oil-phase as well as in cleansers as it also works with most cleansing agents (unlike a lot of other thickeners).