1. to pronounce sth clearly and distinctly
articulate your position/instructions/conditions
As a verb, 'to articulate' means to be clear in your speech and diction so that you are easily understood. To 'articulate clearly' is the opposite of 'to mumble'. This can be used in social and professional contexts but you are more likely to hear it used in formal situations. Similar words include 'diction' and 'eloquent'.
2. having or showing the ability to speak fluently and coherently
an articulate speaker/presenter/manner
This is an adjective describing someone who speaks fluently and without hesitation. This adjective can also be used to describe a speaker or someone who gives cohesive and engaging talks or speeches. You can use this in social and professional contexts but it is more likely to be used in a formal or professional context.