Explain = make something clear by giving relevant facts or more detail
Articulate = to say something clearly and coherently. This might include the way you pronounce it. So the actual sounds of the word(s), for example:
"English speakers may have difficulty articulating Sri Lankan words or place names."
But because it can also be about coherence, people also use articulate as a synonym for explain - for example:
"He was determined to articulate the problem."
I hope I have articulated/explained that properly ;-)