Vector graphics doesn’t consist of separate pixels but of vector objects. Vector objects are a description of the picture. They specify for example, that there is a circle with radius 50 at the position (100; 100) and a line should be drawn from (10; 10) to (100; 50). Theses line strokes, that build up a vector graphic, are called path. Each part of the path, that has a starting point of its own, is called subpath. I.e. a vector object, that consists of two rectangles, has two subpaths.
Each of these objects can be assigned a line style, a line color and a fill color.
Vector graphics is well suited for diagrams and for stylized graphics like pictograms.
Vector graphics has the advantage that it is easily resizable without loosing quality. Furthermore non-complex pictures need significant less memory if stored as vector graphics.
The disadvantages are that complex vector graphics is harder to create and that vector graphics is slower to draw, because the computer has to calculate its look.