I have calculated NDVI, now I would like to measure the distance from the places which have more vegetation concentration to low to bare concentration areas. which tool in ArcGIS 10.2 will be suitable to measure the distance (in metres)?
First you need to Reclassify your raster based on NDVI values, like if NDVI is greater than 55 then that is vegetation otherwise no vegetation. However this marks any low lying cells as vegetation, grass, paddocks, etc. not only trees. Then, if your places are in vector format (e.g. point, polygon) I would use Buffer tool with a buffer distance of preference and run Zonal Statistics as Table tool to tally land cover according to Reclassify-ied raster values.