With the properties of chelating metal ions, increasing protein water holding capacity, PH buffering, stabilization, emulsification, casein thickening and ect, tetrasodium pyrophosphate is widely used in food to improve the gel strength and the tenderness of meat products/analogs.

Also, it is used with other phosphates (e.g. sodium hexametaphosphate, sodium acid pyrophosphate) in seafood to increase the water retention.

Food
Food grade TSPP is mainly used in following two functions:

A buffering agent: with the PH value from 9.8 to 10.8 (1% solution), TSPP can be used as an alkaline to adjust pH in processed food, pudding and etc.
A calcium sequestrant: TSPP can remove naturally occurring calcium ions from proteins and crosslink with proteins, which results in accelerating protein gelation, improving texture (mouthfeel) and reducing cooking loss in meat analog production (e.g. soy protein).  
Following food list may contain TSPP:

Meat analogs, such as soy or wheat based food, with the appearance, flavor and mouth-feel the same with meat but not made from meat.
Marshmallows
Pudding
Cheese
Ice cream
Milk protein products
Tuna
Toothpaste
Orally the main purpose of TSPP is to prevent the formation of calculus by reducing the deposition of calcium and magnesium on teeth. Thus it is commonly used as the anticalculus component of many tartar-control toothpastes and mouth rinse. Disodium pyrophosphate also has the same function.

The top toothpaste manufacturer, Crest also uses it as the anti-tartar ingredient in its whitening expressions.