Speed is relative. How fast is Earth moving relative to what?
The Sun? -- 66,000 mph (107,000 kph)
The center of our Milky Way galaxy? -- 486,000 mph (782,000 kph)
The Local Group? -- 673,000 mph (1,083,000 kph)
---
Earth is moving at a constant speed through the universe. You don't feel movement when you're moving at a constant speed. You only feel a change in speed, which is acceleration.
The same reason you don't feel movement on a airplane, because the airplane is travelling at a constant speed, not acceleration.
---
If you're really interesting in learning some more about what you have just asked, search on Youtube for "Special and General Relativity" - it will give you a true understand how speed works.