You can really tell on a push mower if something is out of whack. When you start up the mower on a concrete surface and it wants to jump around rather than sitting in one place. This is a sign that something is out of balance. You could have hit something with the lawn mower blade and bent either the blade or the crankshaft on the mower. You could also have a cracked blade or a piece missing from it.
You could also have a loose lawn mower blade that is causing this vibration. It is something that is rotating and is not in proper alignment that causes it to vibrate excessively. This rotation will cause it to jump from side to side and can be dangerous if the mower gets out of control.
This vibration situation should be checked out as soon as possible to see what is causing it and a repair recommendation. A small engine repair shop can identify what this issue is and find a solution for you so that your lawn mower will be safe to operate once again.