Positive carry is a profitable difference between the income from an investment (which exceeds) the cost financing the investment.
The importance of carry varies. Some strategies rely on positive carry to make a profit, examples of this include both covered and uncovered interest arbitrage. Carry provides no significant benefit for many strategies is a cost of many others: many strategies are used expecting negative carry.
There are many asset classes where carry may be positive or negative depending on circumstances. Examples include property (carry depends on interest rates and rental yields), investments in bonds funded by borrowing (cost of borrowing versus the coupon paid by the bonds).
Strategies that rely on positive carry to make a profit include both true arbitrage and arbitrage like strategies. In some cases, as with covered and uncovered interest arbitrage, there are both hedged and unhedged ways of exploiting the same mispricing. Many of the arbitrage like strategies are also called arbitrage — with a qualifier that makes it clear that they are not really arbitrage.