Every shape in Illustrator is a path, and every path is made of the same few parts. An anchor point marks a place where the path is pinned down. A segment runs from one anchor point to the next, straight or curved. A curved segment is steered by direction handles, the thin lines with a dot at the end that stick out of a point, and the length and angle of each handle decide how the curve leaves one point and arrives at the next. That is the whole kit. Adobe's help sorts anchor points into two kinds, where a smooth point lets a curve flow through it and a corner point makes a sharp angle.
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