Thick condoms are condoms manufactured from a slightly heavier material, latex or otherwise. Some people prefer thicker condoms for their added strength, as they are less likely to break. An intact condom is of course more likely to prevent unwanted pregnancies or disease transmission.
Some men find they can last longer during intercourse with the somewhat desensitizing effects of a thicker condom. Thus, they are often used as an aid to prevent premature ejaculation.