The Vertex Editor in QGIS is displaying x,y coordinates of the nodes in longitude and latitude. Is there any way to make it display the x,y coordinates in meters?
Vertex Editor simply shows the coordinates according to the Data Source (your layer's) CRS. This is useful, but can cause confusion especially when your project is 'on the fly' (OTF) mode.
Let's say you have 2 layers, one is in NAD83 (EPSG: 4269) and another is in NAD83/UTM zone 17N (EPSG: 26917).
When you select NAD83 layer and activate Vertex Editor it shows Latitude/Longitude. Then you switch to NAD83/UTM17N layer, it shows X,Y in meters.
Your data now has geographical coordinates (latlon). Please reproject your layer by
Save As command to appropriate CRS in meters.