That depends on what the serving is made of.
If it's a serving of grains, it would be 1/2 cup of rice, pasta, or hot cereal (oatmeal, etc.), or 1 cup of ready-to-eat cereal (cheerios, lucky charms, etc.).
For vegetables, it's 1/2 cup of raw or cooked veggies (broccoli, cauliflower, etc.), or 1 cup of leafy raw vegetables (spinach, kale, etc.).
A serving of fruits would be 1 cup of fresh fruit or 100% fruit juice, or 1/2 cup of dried fruits (raisins, dates, banana chips, etc.).
Dairy actually has 3 sizes; 1 cup of milk or yogurt, 1 1/2 cups of ice cream, and 1/8 to 1/4 cup of cheese.
Proteins have even more serving sizes. For lean meat, poultry, or fish, it's 1 cup (when converted from ounces), for cooked beans, the serving is 1/4 cup. The serving for nuts or seeds is 1/16 cup, and then there's eggs and peanut butter, which can't be measured in cups (1 egg, 1 tablespoon of peanut butter).
Oils are measured in teaspoons because the serving size is so small.