Since UE is a game engine and not just a glTF player, it expects you to do some extra animation setup: what animation you want to play and how you want it to be played and controlled.
There are different ways to animate character in UE.
Simplest way to see your animation would be to have your model as a skeletal mesh actor in the scene, and making it use the animation sequence as animation asset.
Basically you tell UE, for this skel mesh actor I want to animate using that animation sequence asset, and I want it to play on start and loop. Then you have to hit the Play In Editor button in the UE UI to see your character move.
If you import into content browser (asset import)
- You do not have any actor in the scene, so you would drag and drop the skeletal mesh asset in the scene or the animation sequence
- If you drag the skeletal mesh it will create a skel mesh actor but it will not set up the animation at all, you have to go and set it up manually as shown in the screenshot
- If you drag the animation sequence it will present your skel mesh actor as shown
If you import with the File>Import into level, UE will spawn the skeletal mesh actor into the scene but again do not presuppose what you want to do with the animation so lets all the animation settings empty for you to set it up.
You might want to have the animation play all the time on a loop but you might also want to use an animation blueprint that will switch and blend animations on your character based on user inputs for example.
More details here.