The phrase often suggests someone is not eager to give money or information. He finally coughed up the name of the accomplice after hesitation.
Pro Tip 2/3
Casual Tone
Typically used in informal situations, not in formal or professional contexts. Come on, you lost the bet—cough up the ten bucks!
Pro Tip 3/3
Pressure Implied
It can hint that there was pressure or persuasion for someone to give what's asked for. After much nagging, he finally coughed up his share of the rent.