Depending on the animation environment, every “frame” is drawn by replacing the entirety of a frame with new pixels. In other words, there is typically no reference within the animation environment to any pixel information from the previous frame/s. Instead, if any data from a previous frame needs to referenced again, the animator/developer needs to create a specific reference to include that previous data in future frames.
Depending on the environment, this can be accomplished in various ways. As an example in P5.js and Processing these programs build visuals by creating a canvas where everything is composited together, UNLESS the developer adds a background() function, which then overlays the background with a color or image of the developers choosing.

If instead the animator/developer wants to create a fading effect, where the previous frame/s are present, but fade over time. They can include an alpha value in the background function (background( red, green, blue, alpha)), which will cause the previous frames to “fade out” over time (dependent on the alpha value).
This approach by P5 and Processing create an easy way for animators/developers to create an animation reference to previous frames. The problem with this approach is that you cannot choose which elements or individual objects include a reference to previous frames, and which do not. Instead, it is a take it all or nothing approach.
In TouchDesigner, each frame is always drawn “freshly”. Unlike P5 or Processing, developers/animators need to specifically create a reference to previous frames or objects if they want to generate animations with “history” or reference to these previous frames/objects.
In TouchDesigner, this is accomplished through the Feedback TOP.
The following video does a really nice job of introducing this relationship between feedback and animation within TouchDesigner.
The video admittedly moves quite quick for a beginner tutorial. So the following breaks down these steps a bit further.
0.01 for both dimensions.
On.
    
noise1 CHOP.Period parameter to 3 and the Amplitude parameter to 0.5.
noise1 CHOP and alter the valuesnoise1 CHOP by copying and pasting.Seed parameter value so they are “out of phase” with each other.
op('noise2')[chan1]noise2 operator, and from its channel array, select chan1.
circle1 TOP.null1 TOP.comp1 TOP to “Over”
null1null1feedback1 also to comp1
comp1 in the feedback1 TOPcomp1 TOP onto the feedback1 TOPfeedback1 parameter window to comp1
comp1 TOP.ONalpha channel parameter for the background color to 1null2 TOP.
feedback1 TOP, click the “Pulse” button in the parameter window.
feedback1 and comp1 TOPs.Opacity parameter value. (notice how different values effect the emergent work)
Now that you have the basic network setup, please try and play with some of the other examples demo’d in the video above.