The answer to 'carpet pet stains' is that common causes include urine, feces, vomit, or other pet accidents. Symptoms can include visible stains, odors, and discoloration in the carpet. Solutions depend on the type and age of the stain, but typically involve blotting, cleaning with an enzymatic cleaner, and possibly deep cleaning by a professional.
For fresh stains, it's best to blot up as much of the spill as possible with clean, absorbent towels. Then use an enzymatic pet stain remover to break down the organic matter and odor. For set-in stains, you may need to rent a carpet cleaning machine or call in a professional carpet cleaning service. They have specialized tools and solutions to deeply clean and extract the stain from the carpet fibers.