I have a mesh, which in edit mode looks as follows
But when I go to object mode, it becomes this
Could someone help me with this? Here's the .blend
file
Your object has Shape Keys (Properties / Data / Shape Keys). One of them, "mouth_U" has a value of 1.00, which mean it is fully "active". Set it's value to 0.00 to resolve your problem.
I guess you've used as a base, a mesh with an armature and a complete facial rig. It's probably safer to remove all Shape Keys and Vertex Groups, before running into other problems.