Trigger Finger is an inflammation of the tendon(s) that flex or bend the finger(s). The flexor tendons travel through the palm and into the fingers. The tendons act as cords that pull the fingers down into a fist and then relax as the extensor tendons on the back of the hand straighten the fingers. As they travel through the palm, they glide through a thin sheath of material lined with lubricating synovium that aids in smooth movement. The tendons pass through a series of pulleys that hold the tendons close to the finger. Anything that reduces space inside the tendon sheath or that compresses the space it moves through, can cause the tendon to get stuck as it goes through the pulley.
Think of the tendon as a line on a fishing rod and the pulleys as the eyelets that keep the line in contact with the rod as it bends and straightens. A knot in the line may make the line catch as it is pulled through the eyelet. If the knot keeps getting larger or the pulley gets tighter, eventually it will be too large to slide back in the other direction and the line will be stuck. That is what happens to the tendons. They simple get too large to move back and forth through the pulleys.