Model order is the type of model used to show a trend in the data. The model order is an important factor in how accurately the model describes the data and predicts a response.
For example, a linear model can show a steady rate of increase or decrease in the data. A quadratic model (often approximately in the shape of a U or an inverted U) can explain curvature in the data. A cubic model can describe a "peakandvalley" pattern in the data.
Model order  Example 

Linear Y = b_{o} + b_{1}X (first order) 

Quadratic Y = b_{o} + b_{1}X + b_{11}X^{2} (second order) 

Cubic Y = b_{o} + b_{1}X + b_{11}X^{2} + b_{111} X^{3} (third order) 
Each model order corresponds with the degree of the equation (the highest power of the X variable) used to generate the model, where Y is the response, X is the predictor, b_{o} is the intercept, and b_{1}, b_{11}, and b_{111} are the coefficients.