Intelligible = that can be easily understood ;  clear to the mind.

• When you address primary school students, use only the vocabulary intelligible to them.
• Due to some interruption in the telephone only some of his words were intelligible.
• His speech was intelligible even to the laymen.
• Intelligible speech/explanation.

Intelligent = having ,showing intelligence ;  brilliant.

• Reshma is a very intelligent and hard-working girl.
• He had a few intelligent things to say on the subject.
• He writes intelligently about the current political situation.
• An intelligent boy/question.