1. Binder / Stabilizer – Retains the physical characteristics of food/cosmetics and ensure the mixture remains in an even state
2. Emulsifier – Allows water and oils to remain mixed together to form an emulsion, such as in mayonnaise, ice cream, and homogenized milk
3. Gelling Agent / Thickener – Increases the viscosity by thickening the liquid to give it more texture
It is a constituent of many non-food products, including toothpaste, laxatives, diet pills, water-based paints, detergents, textile sizing, and various paper products. It is also used extensively in gluten free and reduced fat food products. In laundry detergents, it is used as a soil suspension polymer designed to deposit onto cotton and other cellulosic fabrics, creating a negatively charged barrier to soils in the wash solution. 
It is used primarily because it has high viscosity, is nontoxic, and is generally considered to be hypoallergenic as the major source fiber is either softwood pulp or cotton liner.
It is approved to use as food additive in EU (E466) and US.
Recent Findings :
Sodium Carboxymethyl Cellulose is harmless physiologically and that feeding tests on animals had no signs of adverse health effects.  
Scientific References :
1. PubChem: https://pubchem.ncbi.nlm.nih.gov/compound/6328154
2. Physiological Action Of Sodium Carboxymethyl-cellulose on Laboratory Animals and Humans. (Journal of Food Science, 13(1), 29–35. doi:10.1111/j.1365-2621.1948.tb16591.x)
3. The chemical and physical properties of carboxymethylcellulose and its salts. (J. Chem. Technol. Biotechnol., 60(10), 254–258. doi:10.1002/jctb.5000601004)
Regulatory References :
1. EU Approved Food Additive 
2. US FDA Generally Recognized As Safe (GRAS) Food Substances