What is the unchanged image in Rip Van Winkle? What is its meaning?

This is a bit of a tricky question, because the narrator emphasizes that everything has changed in the village. The question might be referring to one of two things -- the mountain scene, or the portrait on the sign of the inn. Let's look in more detail.
When Rip arrives at the village, he sees immediately that change is everywhere ("everything is strange"), and it makes him doubt himself:

"…he began to doubt whether both he and the world around him were not bewitched."

But Rip confirms that it must be his old village when he looks back at the one thing that hasn't changed -- the mountain scene:

"Surely this was his native village, which he had left but the day before. There stood the Catskill Mountains—there ran the silver Hudson at a distance—there was every hill and dale precisely as it had always been. Rip was sorely perplexed."

If that's the "unchanged image" indicated by your question, then its meaning is that Rip really is back in his home village.
Alternatively, your question may be referring to the portrait on the sign for the "little Dutch inn." At the beginning of the story, this is noted to be "a rubicund portrait of His Majesty George III," the ruling king. Later, when Rip returns and discovers that the village has changed, he sees the sign again, and it still has the portrait on it. But the portrait has been altered:

"He recognized on the sign, however, the ruby face of King George, under which he had smoked so many a peaceful pipe; but even this was singularly changed. The red coat was changed for one of blue and buff, a sword was held in the hand instead of a scepter, the head was decorated with a cocked hat, and underneath was painted in large characters, General Washington."

It seems that the inn keeper changed the appearance of the man in the portrait in order to keep up with changing times. The village is no longer subject to King George. Now it's part of the United States. By altering a few details, the inn keeper can now claim it’s a portrait of the President, not the king. Perhaps he made these changes to save money and fuss -- it saved him the trouble of having to hire someone to paint an entirely new portrait of George Washington.
So the meaning in this case is that we have confirmation that Rip has overslept for many years. He fell asleep before the Revolutionary War, and woke up afterwards.