Thickening nail on the foot?

Fungus or trauma. Thickening of the nails is either from a fungus, repetitive trauma to the nail, or both (i.e. Repetitive trauma creates opportunity for fungus to get under the nail). Go see a podiatrist, who can take a sample of your nail and send it as a biopsy to find out if it has a fungus. Then you can start appropriate treatment.
Many possibilities. Some causes of abnormal nail growth include trauma, infection, side effects of medication, and possible systemic diseases such as psoriasis. Have them inspected by a professional to determine the cause of the problem, as treatment varies depending on the diagnosis.