For example, Twitter employees can quickly ballpark the dollar value of their shares with the $26 number. It's also easier for tracking movement (e.g., $20 last week, $26 this week).
It's the same reason that all ticker prices are in per-share value rather than market cap. $XOM at $93.22 means less to me personally than "Exxon Mobil is worth $400 billion," but the per-share value is probably most relevant to people with business interest in Exxon.
Sure, the price doesn't matter much to a retail investor. But millions of shares will be bought tomorrow at that price so it certainly means something to the right people.
Twitter Prices IPO At $26 Per Share
or
Twitter Prices IPO At $18 Billion Valuation
Before Berkshire Hathaway issued a stock split (1 share becomes 2 or more shares) a share was worth ~$172,000. Today Apple trades at $520 and MSFT at $38.
Alone those numbers are of no use. You don't know how much the actual company is worth. Share price * share volume = Market Cap. You need to know at least two of those values to make an informed decision.
Of course anyone with a bit of sense knows that it's not the individual share price that matters; but with something as famous as Twitter, that is not necessarily who you are marketing the IPO at.