Profiting from legal loopholes[1], esp where two things accomplish the same goal, but one of them is more vigorously enforced/regulated than the other.
In this case, both taxis and limo/livery services[2] provide the same good -- "rides to somewhere" -- but taxis are more regulated in terms of rate, driver training, equipment, and how many can be active (medallion limits). Limo/livery services (or something passed off as one), by contrast, are less regulated, and what regulations they have aren't as closely monitored because (until recently) no one cared.
The analogy to arbitrage is that it's a case of same good, but different prices on different "markets". (Whether you market it as a "livery" or "taxi" service.)
Side note: IMHO, such arbitrage can't fully account for the success of Uber/Lyft, which have actually obeyed the major "no street hails" rule. They provided a better service (reliability and seeing when your ride is coming), squeezed out enormous efficiencies from harnessing IT, and solved major public goods/incentive problems that the regs were failing at -- how to fairly allocate the undesirable fares and get people to provide feedback on bad drivers.
[1] http://www.investopedia.com/terms/r/regulatory-arbitrage.asp
[2] The legal difference between the two is that a taxi can do street hails -- on-the-spot arrangements found by line of sight -- while limo/livery services must be pre-arranged through some booking service that logs the specific driver/vehicle assigned to chauffeur a specific person + guests to another place.