The most prominent standard library used for writing interactive 3D graphics applications is OpenGL. OpenGL is cleanly and well designed and has a very specific goal: be a layer on top of the graphics hardware, as thin as possible, as thick as necessary to abstract away the differences between different graphics hardware variants.
A consequence of this design is that OpenGL is very fine-grained and flexible. Every object has to be specified vertex by vertex including all its data. Newer OpenGL functions (e.g. Vertex Arrays) simplify this somewhat, but only in a limited sense. The closest thing to an object in OpenGL is a display list, which is just like a macro recording of the executed OpenGL commands, and don't feature any object-specific interface.
The idea of a scene graph is to provide a higher level of abstraction. A scene graph actually stores the whole scene in the form of a graph of connected objects.
Example Scene's Graph
Graphs are used in many places in computer science, scene graphs are a subset of general graphs. They are acyclic, i.e. there can be no loops in the scene graph, as they would lead to infinite loops when trying to walk the graph. They are directed, i.e. there is a defined direction of the connections between the nodes. Thus nodes can be grouped together by attaching them to a parent node. This conceptually allows manipulation of a large number of nodes by manipulating this parent node. Of course this is recursive, i.e. these parent nodes themselves can also be grouped and attached to another parent. In the end this leads to a single root node, which defines the whole scene to be rendered. In general there can be more than one graph in an application, but whatever is displayed in a single window is usually defined by a single root node.
One aspect that scene graphs make more explicit than OpenGL is the sharing of data. It is desirable to use the data of a node in multiple places in the graph, e.g. store only one copy of the wheel's geometry and use it in multiple places. The disadvantage of the simple multi-use is that it is not possible any more to identify a single wheel, as they are all the same object. Thus OpenSG uses a different method to do sharing, the Node-Core split, see Nodes & NodeCores.
Scene graphs, in contrast to many other graphs in computer science, are also heterogeneous, i.e. there are many different types of nodes with different functions (see Nodes & NodeCores for the different types OpenSG supports). There are two general types of nodes: groups and drawables.
Groups (see Groups) are used to structure the graph into parts and to control either attributes of their subgraph (e.g. Transform) or to select only a selection of their children for traversal (e.g. Switch).
Drawables (see Drawables) are usually put in the leaves of the tree (i.e. they have no children) and contain the actual elements to be rendered. In most cases this will be polygonal geometry (see Geometry), but other types are possible (e.g. Particles or Slices). The parameters that define the surface charaterictics of the rendered objects e.g. surface color, shininess or texture (or rendering paramaters in general, as some Drawables don't have a surface) are usually associated with the Drawable wrapped in a separate object, in OpenGL it is called Materials. This Material can and should be used by as many object as possible, to get good performance.
I hope this page can give you a first rough idea of what scene graphs are about.