Elastic connective tissue is a technical term for body tissue that contains a large amount of elastin, one of the proteins that make up connective tissue in general. Elastin is the protein that allows for tissue to regain its shape after being compressed or warped.
Elastin is springy. Large amounts of it are found in the arteries and lungs, which allows them to take in and move large flows of blood and air, respectively.
Elastin is also important for cushioning the body against heavy loads. Large amounts of elastin are found in the elastic ligament of the spine. This ligament is also known as the ligamentum flavum, because elastin is yellow. "Flavum" is Latin for yellow.
Collagen, the other main protein that makes up connective tissue, provides rigidity and structure.