…,how did they turn 2D sprites into meshes?
I would assume they created the 2D meshes using a tool such as Autodesk Maya or Autodesk 3DS Max. The tool only needs to be able to export to an FBX file format - one that is owned by Autodesk meaning it is licensed. From there you simply create a 2D plane, attach a material to said plane, and apply a texture (the sprite). There are numerous settings you can apply to your exported mesh, but that isn’t for this answer. If you would like to read more into the static mesh pipeline, this link will provide the information you’d need about import settings provided by UE4.
Once you’ve exported the mesh as an FBX file, all you need to do is import the FBX file into your project via the editor. With the appropriate import settings selected, the editor will create the object for you. The 2D mesh will be imported as a static mesh object. From there, you can use this static mesh as the starting point for a character with animations or as environment sprites. However, to animate a static mesh, you’ll need to create and apply a Material Instance Dynamic (MID) to the mesh in order to change what texture it is currently displaying (which sprite on the character sprite sheet). To see how you might do that, I would recommend looking at the Tappy Bird project specifically at the MainGame Blueprint’s Construction Script and Event Graph (the MID creation and Animate chicken sections respectively).
If you don’t have Autodesk Maya or 3DS Max nor the means to acquire a student/licensed copy, then I would recommend using Blender. The developers at Epic mentioned they were working with the developers of Blender to enhance the FBX exporting tool.