Most grout is like this - especially coloured (non cement grey) grout.
What kind of tile do you have laid? you can use a mild acid cleaner like lithofin cement residue remover and a white emulsifier pad to take a tiny layer off the top of the grout. You have to dilute the cleaner quite heavily and you should try on a small area first to ensure you wont get any tile damage (unless you can confirm the type of tile to me).
Once cleaned you can seal the grout using another lithofin product to stop this happening again.
If you are trying to fight fat stains on floor. Please try simple household items like vinegar or baking soda if the stain persists try generic household cleaners such as Mr. Clean, Lysol, or powder-based cleaners. the next trick is to use commercial tile and grout cleaner. I hope this will help Thanks.