It depends a little bit on what you want to do - should the mesh be moving in Edit Mode so that the origin of the object stays where it is or do you want the object to completely move, keeping the origin at its relative position to the mesh? Possible ways to achieve some of these results:
First of all make sure the Snapping is set to Vertex.
Now you can activate the Cursor tool, this way you can drag the 3D cursor wherever you want by holding down LMB. If you hold Ctrl while dragging (but you have to start dragging without the key), you can snap the cursor to the vertex which you want to place in a specific location later on. You can do this in Object Mode or Edit Mode. Deactivate the Cursor tool again to make sure you are not accidentally moving it for the next steps.
Switch back to Object Mode if you are not already. You can now select the object, right-click and choose Set Origin > Origin to 3D Cursor if you don't mind the origin changing its position. Then simply enter the specific location in the XYZ Location to move the whole object.
Instead of changing the origin, you can press Shift+A > Add > Empty to place an empty at the position of the 3D cursor, and therefore where the vertex is. Then first select the object, Shift + select the empty, Ctrl+P > Set Parent To > Object. Now the object is a child of the empty and you can move this to the specific XYZ Location and the object will follow.
If you want to keep the origin where it is and only move the mesh in Edit Mode, you can use this method: select the vertex which should be placed in the specific location. Press Ctrl+H > Hooks > Hook to New Object. This creates an empty at the location of the vertex.
While still in Edit Mode, hit A to seelct all vertices now. Go to the modifiers, there you will find a Hook-Empty modifier. Press on the button Assign. Now all vertices are hooked to the empty. Switch back to Object Mode and now you can move the empty to the specific location, the mesh will follow while the origin stays where it is.
Combinations and variations of this method are possible, too. For example, if you do not want to move the 3D cursor but want to parent the object to an empty in the vertex position, select the vertex and hook it to an empty. But then delete the hook modifier and just parent the object to the empty like described earlier.
And for completeness to have a visual reference for FFeller's (second) method: set the Transform Pivot Point to Active Element at the top, make sure the vertex which determines the position is the active one like the highlighted white one in the image below (either by selecting it first, then all others with A or Shift-selecting it last). Place the 3D cursor in the desired location by entering the XYZ values in the View tab of the sidebar. Then press Shift+S and choose Selection to Cursor (Keep Offset). The Keep Offset part is important, otherwise all vertices will fall together in the same location. This method also moves only the mesh while the origin stays in place.