(Intercept):Measurements is the "main effect" of measurement type--a factor with 4 levels in this example (i.e. length and width of sepals and petals). The significant F for this line indicates that the average values of these 4 types of measurements differ.
species:Measurements is the term for the interaction of species by measurements. The significant F for this line means that the patterns of differences among the 4 measurement types differ across the three species. Equivalently, it means that the pattern of differences among the three species differ across the four measurement types.