“会(huì)” is an auxiliary verb. It  means “having the ability to do something, /having a kind of skill, or it indicates a simple future tense.
For example:
Wǒ huì shuō Hànyǔ.
我会说汉语。
I can speak Chinese.
Míngtiān huì xià yǔ.
明天会下雨。
It will rain tomorrow.

“可以(kěyǐ)” is also an auxiliary verb. It means “can, may.” It is usually used to show a request or permission to do something. 
For example:
Nǐ kěyǐ bāng wǒ mā?
你可以帮我吗？

Can you help me?
当然可以。
Dāngrán kěyǐ.
Of course I can.