Well the regression function you have might look something like this:
aox lovel = a + b(Temp) + c(Steep) + d(Steep^2) + e(Temp*Steep) + f(Temp*Steep^2)
Where Temp, Steep, Steep^2, Temp*Steep, Temp*Steep^2 are predictor variables, and "aox level" is the outcome variable. We say that this function is linear in Temp since it only has a power of 1. Likewise, this function is quadratic in Steep because it has a Steep^2 term. There is also a linear Steep term. Each of the b, c, d, e, f are an indicator of the relationship between the corresponding predictor variable and aox level. If one or more of the b, c, d, e, f are equal to 0 then there is not a relationship between the corresponding predictor variable and the outcome variable. The p-values in the table above are the result of a test to see if these b, c, d, e, f are zero. If the p-value for Steep linear corresponds to a test for c = 0. Since the p-value is less than 0.05, we conclude that c is not zero. We say that there is a "significant linear response in Steep" because c, which corresponds to the linear Steep term is significantly greater than 0.
The same type of argument can be given to squared terms like Steep^2. We say that there is/is not a significant quadratic response in Steep. If there is a Steep^3 or Steep^4 term in the model, we would say something about the cubic or quartic response in Steep.
Hope this makes it a little clearer.