Enterprise value is simply the market value of operating assets of a company. it can help if your trying to gauge relative values quickly between companies, commonly divided by EBITDA (which is the cash flow generated by the assets) as a quick multiple. Yes, it can br useful ....... BUT.... like all metrics that depends upon how you use it.
EV / shares outstanding would give you EV per share.
I'm not sure I understood RandR's definition. EV is market cap plus debt (and other bits and pieces), minus cash. Meant to be a hypothetical figure of what you would have to pay to buy out the whole company. i.e. You'd have to take on the debt as well as pay the market cap. You subtract the cash because of course if you pay $1m and get 100k cash back - you've only paid $900k.
EV is essentially incorporating debt into the valuation of a company.
EV per share (which was your question) would simply give you that valuation on a per share basis.