If you can’t see sharply close to, your eye’s closest focus distance is too far away. Adding a small positive lens in front (or less negative if you are already short sighted) brings the close-focus point nearer to you, so reading distance is within the range that your eye can adjust focus to see clearly.
Reading glasses usually address presbyopia, which is hardening of the lens. The glasses themselves are convex shaped which makes objects closer to you look clearer. It doesn’t only magnify the object you are looking at.
AS you may have guessed, regular glasses are concave which addresses nearsightedness (so you can see far away objects a bit better)
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