Nobody can tell you anything without proper details like the relavant layer switches, preview settings, render settings, version of AE, system info. Provide screenshots and the required info.
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If you've turned on the Motion Blur switch on the layer, and you've enabled Motion Blur for the comp, toggling on the switch at the top of the timeline, it could be that the layer isn't moving very quickly. You can still get it to blur in Comp Settings > Advanced > Shutter Angle. It defaults to 180 degrees, but you can increase that to something that can't exist on a real-world shutter angle, like 720 degrees.
Play with it. see if it helps.
If you are just animating position of a still image Motion Blur should work unless you are using Ray-traced rendering on a 3D layer. Just make sure everything is turned on. If that does not fix the problem then we need to see your comp with the modified properties of the layer causing problems revealed. Press the U key twice, make sure all columns are visible in the timeline and we can see the comp panel.