This quote comes from the first of Paine's "Crisis" pamphlets, written in December of 1776 as the Americans fought the British for independence. It was meant to inspire people and shore up the morale of the troops, to whom it was read aloud on December 23rd, 1776. It was also meant to stiffen the spines of Americans who remained on the fence about the revolution.
Paine was a fervent supporter of independence, equating British rule with slavery. When he states that "what we obtain too cheap, we esteem too lightly," he is trying to cast a possibly long war in the best possible light.
When he says what we "obtain too cheap," he refer to an item that doesn't cost much money or that we paid less for than it was really worth. When he says we esteem such an item lightly, he means it matters very little us. Esteem is respect, so if we buy something cheaply we don't respect it very much.
Paine is applying this maxim to the Revolutionary War. He is saying that if the Americans were to have obtained a victory and independence months ago, they wouldn't value it as much as they will once they get it after a long struggle. Paine is in no doubt that the Americans will win, but he knows the people need to hear words of inspiration that will encourage them to stick it out over the long haul, so he provides those words.