In the video, "What is Illustrator," the speaker quickly talks about use uses Illustrator and why. Illustrator is mainly used by artists and graphic designers but almost anyone can use Illustrator for anything they need. Illustrator is used to create Vector images that are scale-able that will be printed or used on the web, this includes freehand drawings, tracing and recoloring images, creating wire-frames for digital paintings, designing logos and icons, and even website mock-ups. Illustrator can also integrate with other Adobe applications such as InDesign, Photoshop, Flash, and Aftereffects. Anyone, from a professional artist to someone looking to create a business card can use Illustrator.
The second video, "Understanding Paths," simply talks about how all the Vector artwork created in Illustrator is made up of paths, this does not include what is on the inside (such as the stroke and fill) but the "skeleton" of the image. For example, a rectangle created in Illustrator is made up of four different paths connected at the corner by anchors (the subject of the next video summary). In order to see these paths, click "control y" and you will be able to see the underlying structure of the image in Illustrator, to go back to the actual appearance, just click "control y" again.
The third video, "Understanding Anchor Points," then talks about the "joints" of each path and what they are for and how they work. The anchor points in a path control the direction, position, and behavior in relation to other paths inside the artwork. When an anchor point is selected it will appear blue, then all you need to do in order to manipulate the path this anchor is connected to is click and drag the anchor point selected. Curves in a path have anchor points has well that are accompanied by control handles. You can used these handles to change how the path is curved when selected.
Paths and anchors are what make up everything you see and create in Illustrator, they are the backbone of every image. Once you get the hang of creating paths and changing them by using different anchor points, you can create almost anything.