Fairings, also known as ease-ins /outs, slow ins / outs....whatever you want to call them, you need them in your animation software! Fairings are about interpolation - or in plain English, how you either accelerate or decelerate from one key frame of animation to the next.

Take a simple example of animation: suppose we want to animate a scene in which a car begins a journey. First the car is at rest, then a few seconds later it will be up to speed. But it does not go instantly from one state to another; it will accelerate from being static to its cruising speed. This acceleration is one kind of fairing.

The ink and paint program Animo deals with fairings very comprehensively, so I have grabbed screen shots from it to illustrate things.
Here is how you represent a linear move between two key frames in Animo and it shows a case where there are no fairings:

The starting frame is at the bottom left and the end frame (in this case, frame 16) is at the top right. As you move across the graph from left to right, you are progressing in time. As you move up the graph, you are altering a value. This value will very often be the distance of a movement, but it can just as easily be a change in a quality such as colour or degree of blur and so on. By the way, if the line of the graph were horizontal, this value would be the same and this would then in effect be the same as a hold.

In the present case, the graph above shows the movement of our car when it is up to speed and travelling at a constant rate. During these frames, therefore, there are no fairings.

A linear move, as is obvious from the graph above, means that for every frame, every inbetween change is the same amount. This means that each frame (the "fence" at the bottom) is equidistant from its neighbour.

Many movements start slowly, get up to speed, then end slowly (for example, if a character turns their head, the move might well start and end with fairings like this:)

On the other hand, many movements may accelerate from scratch but end suddenly without a fairing. For example, suppose you are animating a hammer hitting a nail. The hammer will move by accelerating until the point at which it hits and it stops dead. For this very common sort of move, you want a curve like this:

The opposite would be a move that only slows. (Say a marble rolls to a halt; it will decelerate throughout the move):

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Note two things about these graphs: first, each control point has a handle with which the animator can "finesse" the move to their heart's content by adjusting the slope of the curve. Second, though not shown here, it is also possible in Animo to add as many extra control points as you want to make very much more complex movements such as oscillations.

The examples above are just basic curves. By altering these curves carefully, a piece of average animation can be given the extra sparkle and flair that makes it special. For instance, by changing the direction of a fairing's curve, you can create an "overshoot" in the animation. Learning how to tweak these fairings is the mark of a good animator.