# Degrees of freedom clarification [duplicate]

I'm new to statistics, and so far I'm not grasping the significance of the concept of "degrees of freedom". So far, I've only had tangential exposure to it by way of calculating Student's t.

When we run anova() in R, in this example, I don't understand why the degrees of freedom are returned (the "Df" column) in this context, and what it contributes:

> tomato <-data.frame(
+ weight=c(1.5, 1.9, 1.3, 1.5, 2.4, 1.5, # water
+  1.5, 1.2, 1.2, 2.1, 2.9, 1.6, # Nutrient
+ 1.9, 1.6, 0.8, 1.15, 0.9, 1.6), # Nutrient+24D
+ trt = rep(c("water", "Nutrient", "Nutrient+24D"),
+ c(6, 6, 6)))
> tomato.aov <- aov(weight ~ trt, data=tomato)
> anova(tomato.aov)
Analysis of Variance Table

Response: weight
Df Sum Sq Mean Sq F value Pr(>F)
trt        2 0.6269 0.31347  1.2019  0.328
Residuals 15 3.9121 0.26081


Some clarification would be greatly appreciated.