To say that Carthage was a commerical empire means that what distinguished Carthage more than anything else was its propensity and success as a trading city. From a historical point of view, Carthage was a Phoenician city. It was the primary city of the Phoenicians, especially as Tyre and Sidon, two other important cities, were destroyed earlier on.
As the former answer stated, the Phoenicians did not create an empire like the Romans, but they remained as cities. Carthage, therefore, was one of the Phoenician cities.
What these cities excelled in was trade. They reached many parts of the ancient world with trade. For instance, the were in North Africa, Greece, Italy, and Spain. As you can imagine, there were also the greatest seafarers in the ancient world as well. As a side note, according to Polybius, the Romans actually learned the art of shipbuilding by capturing one of the Carthaginian vessels. But all of this was under the Carthaginian passion to make money through trade. In this sense, it was not imperialism that governed Carthage but profits through trade.
Carthage is described in this way because it did not actually directly rule most of the places that were part of its "empire."
In a traditional empire, the imperial government has direct control of the various parts of its empire. Rome was like this, with all of its provinces being ruled from Rome. But Carthage was different. The various parts of its empire were mostly independent. They relied on Carthage for defense and did what it said in terms of foreign policy. However, Carthage did not rule them. It traded with them and its wealth made it powerful. Therefore, it was a commercial "empire."