Over the years, 2D animation has become more and more popular due to it's simplicity and it's beautiful results. Unlike traditional animation, 2D animation does not require amazing drawing ability, making it viable for anyone who wants to learn animation. 2D animation is used more and more commonly on things like introductory, story telling and music videos now. The most commonly used application for 2D animation would be Adobe Animate CC, it gives a huge variety of tools for beginners to pick up 2D animation quickly. Another suggestion program that I would give is Adobe Flash, it's really common in web pages and games, and due to its long history, it's also really easy to find tutorials.
Some sample tutorials: