Investors aren't looking at what Square's offering now; they're looking at what Square can reasonably offer in the future, soon enough that their investment is

Investors aren't looking at what Square's offering now; they're looking at what Square can reasonably offer in the future, soon enough that their investment is "worth it". Square may only address 0.01% of the market now, but they might have a realistic plan for addressing 0.1% or 1% or 10% of the market, making them a billion to multi-billion dollar company. If Square is able to convince investors that they've got mass market appeal then they can justify a multi-billion dollar valuation. Considering Visa invested an undisclosed amount in Square, they may actually have reason to command such a large valuation.