If you drive mostly on short, local trips, or on dirt roads, you may need to change your oil often.

The oil needs to be changed "more often". Because, in short and local trips, there are times you have to stop more than you would as compared to a long trip, mostly due to traffic. These doesn't allow time for the engine to warm up properly, thus changing the viscosity of the oil. This will lead to improper greasing of the car parts and eventually damaging of the car. Same goes for driving on a dirt road, the particles in the air can get into the oil and thicken the oil, thus no proper oiling of the car parts.

productive most commonly means: achieving or producing a significant amount or result.

explanation:

productive can also mean:

producing or giving rise torelating to or engaged in the production of goods, crops, or other commodities.

these depend on how the word productive is used. most likely productive will mean   achieving or producing a significant amount or result.