It means you're "aiming" too much. Unless you're shooting slugs, think more of horseshoes and hand grenades--"close is good enough" should be the focus, rather than "line up the sights" exactly on the spot on the target you wanna hit. Someplace around......"HERE"..BANG!! is more how it should feel and look. No more important piece of advice can be given when you're shooting birds (or anything moving at an angle) than: keep the gun moving gently and smoothly-- aka, "Lead the target". You can't 'aim at the chest' on a bird in flight, no matter what direction it's traveling.
Here's two examples:
Imagine an insect flying 45* away from you. Attempt to follow it by pointing your finger at it and imagine that your finger is the nozzle on a garden hose, adjusted to spray a jet stream of water. When you think your finger is lined up with the target, bang, you've squeezed the trigger as the gun stops swinging, and a short 'rope' of water 'chases' the bug.
Now imagine following the insect with your finger, but the garden hose nozzle is adjusted to spray a fan, or cone of water. How would you attempt to hit the insect? Keep the hose moving, leading the insect, and let the entire cone "paint the open space" with one smooth 'brush stroke'-- behind, at, and in front of, the insect in case he changes direction.
Rifle shooting and shotgun bird-shooting are like those two examples. The slower the target, the less you need to 'swing through it' (or, keep the gun moving) as you pull the trigger. The goal with a shotgun is to spread the pellets (whatever their number) through as big a portion of space as possible to obliterate the air that your target is traveling through. The only exceptions I can think of are human targets and large animals; in those cases, leading the moving target is still very important, but generally, their lack of speed requires a much smaller follow-through (swinging, or keeping the gun moving).