According to the Strong's Hebrew dictionary it literally means "Lion of God" it can also be interpreted to mean "Mighty Lion" (Proverbs 28:15; Nahum 2:11;
2 Samuel 23:20; 1 Chronicles 11:22). It can symbolically refer to Jerusalem because the symbol for the Jewish tribe among the 12 tribes of Israel was a lion.
When pronounced the original way it's supposed to sound more like: Ah-ree-EL, or Aw-ree-EL, NOT Air-ree-yell. The former Prime Minister of Israel's first name was also Ariel. Just ask any Jew, they'll tell you.
Otherwise, it makes a nice girl's name when it's pronounced Disney-style.