Something that's elongated is stretched out, or extended so that it's longer than usual. Some painters, like El Greco, are known for their strange, elongated figures.
Things can be elongated because they're literally pulled and stretched, while others are described this way because they are very long and thin to start with. A young woman's elongated neck or your tall, skinny dad's elongated body are both examples of this. The Latin root is elongare, "to prolong or protract," from longus, or "long."