Foxtail are mature seed head that are found in some types of mature grasses that can burrow into a horse's mouth. Acting the same way a plastic anchor does in drywall, the foxtail then can't be easily removed, as the barbs prevent it from being easily removed.
While seemingly benign, horses can eat foxtail found in their hay, and then develop significant ulcers of the mouth, tongue, or lip. Your horse may go off feed after a while as it's painful to eat and chew with a sensitive ulcer being resolved.
How can you help your horse? If you're feeding mature, late season hay, you may see foxtail in the bale. Watch out for those - your best option is to not feed that hay. While not completely realistic, you can try to remove any you can see. Some signs of a foxtail ulceration include an odor from the mouth, difficulty chewing, excessive salivating, and frothing of the mouth. If your horse has already gone off their hay and you suspect foxtail embedded in their mouth, simply stop feeding that hay, and let your horse's body handle the rest. You may, if necessary, use very diluted chlorohexadine rinse to assist in the healing.