An arms-only golf swing is one in which there is not enough rotation from your upper body during your backswing. As there is only a partial amount of rotation from your upper body, your arms do more than they really should and become dominant during your backswing and consequently dominate your downswing as well.
One result of this type of swing is that you will not hit the ball as far as you could when rotating your upper body. You only have the strength of your arms swinging the golf club and this will never deliver as much speed into the club head as rotating your upper body will. Think how you throw a ball. If you stand with your body static and just use your arm, you will never throw the ball as far as if you use your whole body to throw the ball.
Another consequence of an arms-only swing is that you will tend to strike the ball inconsistently from the club face. Using your arms produces a very steep or high backswing and club head position and as a result of this you will tend to hit the top of the golf ball as you are swinging downwards from such a high club head position. If you do not strike the top of the ball, you may strike downwards into the ground just before the ball and end up taking a big divot. Either way though you will find it difficult to consistently hit the side of the golf ball and create a consistent strike.
The final consequence of this type of backswing is in the direction the ball will fly. An arms-only swing will mean that the club remains relatively close to the target line during the backswing. If we look at the movement from sideways on, you can see that the club stays closer to the target line than if you were rotating your upper body. As a consequence, on your downswing the club head will move to the far side of the target line, or the outside and then you will have to pull the club head towards the ball to strike it, producing a movement where the club head travels across the target line (from out to in) rather than down the target line. With this movement, if the club face is pointing in the direction that the club head is moving, left of the target line, the ball will fly left of target. If the club face is pointing at the target, the ball will fly left to right and produce a slice.
To improve an arms-only swing we need to get you rotating your upper body to the right. Initially, put some resistance to the right of the club head, so step off the range mat and use the edge of the mat as the resistance, or if you are at home, set up so that you have a chair or table leg on the right of the club head. Once in your set up position with the mat on the right of the club head, initiate your backswing movement and notice which part of you instigates this. Is it your hands or is it your shoulders? It needs to be your left shoulder moving the club away from the ball if you are going to rotate your upper body correctly during your backswing.
The next drill that I would suggest you try is to set up without your golf club in your hands. Place your golf bag next to you on your right and imagine you have a friend on the other side of this, who is stood in line with you. Reach out towards them with your left hand as though you are going to shake their left hand. Notice how you rotate your upper body right towards them as you reach your hand out. This is the correct movement to have during your backswing. Try this a few times and then hold your golf club and attempt the same movement, working on shaking hands with your left hand. At the top of your backswing your upper body should be rotated as close to 90 degrees right of it's start position as possible, so you should find your back is flat to the target.
Try these drills and you will begin to incorporate your upper body rotating into your backswing and you will see a massive improvement in your connection with the ball, the direction of your shots and the length that you can now hit.