I'm using ArcMap 10.3 on Windows 10.
I have a number of .bil and .tif files pertaining to altitude and weather data. I want to open these in ArcMap. When I attempt to add them to the map I get this dialogue box:

Can someone walk me through how to use this to open these files in ArcMap?
This is the error that I've encountered trying to do this myself:

Or it throws up a generic "can't open this" error. I would share a screenshot of this but I can't replicate the error.
The goal is to use these data to find the average temperature, slope, etc for a number of points (n=157), so I assume I would need the .bil/.tif to have a spatial referencing system. I'm using the Irish Grid coordinate system.
EDIT I used the Define Projection tool on the files and they did change to Irish Grid (when I right click the feature class go to Properties < Source it does say it's in Irish Grid) - but the data doesn't line up with all my shapefiles in the Irish grid, it's "off in space" just the same as having no coordinate system. I tried this with both file types and the result is the same.
.tfwand.blwfiles with your images) you will need to georeference the images yourself. – Midavalo Aug 09 '16 at 19:28