Recall from MAM1000W that you defined how smooth a curve is, that is, does it progress in a “nice” manner from age to age, without too many “bumps”. Think about an exponential function or a logarithmic function - there are smooth. A polynomial of a very high degree, however, will not be smooth (Google a picture of this one).
Now, smoothness refers to the opposite of adherence to data. Let’s say that we plot our crude rates (as shown on the slides), and fit a curve through them. Then, this fitted curve will be very rough and not smooth, but WILL adhere to the data very well (since it passes through every data point). If the curve is less jagged and more smooth, chances are that it will not pass through each and every data point, meaning that we have less adherence to data.
And hopefully this little example illustrates why smoothness and adherence to data are conflicting objectives!