Above and Over have a similar meaning. The both mean "at a higher position than X" but above normally refers to being directly (vertically) above you.
• Planes normally fly above the clouds.
• There is a ceiling above you.
• There is a halo over my head. ;)
• We put a sun umbrella over the table so we wouldn't get so hot.
• Our neighbors in the apartment above us are rally noisy.
Over can also mean: physically covering the surface of something and is often used with the word All as in All over.
• There water all over the floor.
• I accidentally spilled red wine all over the new carpet.