In other words, don't worry about running out of food. "Dearth" simply means "lack." The question might be, however, does Adam even know what "dearth" or "lack" means? Consider Adam as a baby, experiencing the world for the first time. Being in a land where the fruit is always plentiful, a lack of something is an abstract concept to him. We have to assume, however, that when God created Adam, he also gave him a certain amount of knowledge as well.
However, not having to fear "dearth" or a lack of food is important. This is Paradise, after all, and that makes it nearly perfect. The abundance of food is one aspect, but there was more to it than that. Satan, upon seeing Eden for the first time, was quite affected by it.