The lats are the biggest muscle covering your back. They insert on the front and inside of your humerus(arm bone), just below your shoulder. They originate on your iliac crest (pelvis) , your lower ribs, and thoracic vertebra 7-12, and also attach on your shoulder blade.
Their main function is to extend(bring arm down from overhead), adduct(bring arm towards the midline of body), horizontal abduction and internally rotate(turn arm/hand in) your arm as well as help in respiration. But they also resist shoulder flexion, abduction and external rotation. Since they are a strong arm/shoulder extensors, meaning they bring your arm down and back-behind you, lifting your arm and reaching overhead can become a problem when the lats get tight. Their length and ability to stretch are very important for the health of your shoulder as excessive compression will occur in your shoulder when the lats are tight and overworked, creating problem for the normal mechanic of your shoulder and for exemple, often participating in the wear and tear of your rotator cuff.
Another relevant information is that your lats work directly with your butt muscles, your gluteus maximus, and even share some fibers through the thoracolumbar fascia.
the lumbar spine, being a possible source of lower back pain. To counteract this you also need strong abdominals.
A lot of people you see in the gym have very well developed lats, but poor flexibility and they tend to emphasize exercises that will automatically put them in a position where the lats will become tight( chin-up, dead lifts, good mornings...).
A good test to see if your lats are tight would be to raise your arm as far up as you can so your arms are parallel with your head. If you can get them overhead but you have to arch your lower back, rock your pelvis forward or flare your lower ribs to get there, your lats are tight.
Here are my two favorite ways to stretch the lats: