Oh, I know
It looks like a nurbs model (or so I guess).
If this is nurbs then the rendered result has corresponded to your projects level of "accuracy", which is named TESSELATION.
Although the nurbs curves and most importantly nurbs-surfaces, are calculated mathematically and gives that smooth, round shape, the software draws the line for how accuratly the result will be (more "accuracy" "draws" more computing power".
So... there are two menues for setting the tessetation parameters.
1) The first which I usually fiddle with, is the tesselation setting in the attribute editor (Ctrl-A on the keyboard). Default tesselation is 1.5.
2) The second menu is located on the main-menu (while in the rendering mode only), under RENDERING.
("Set NURBS tesselation")
-With "method" 1 pick one nurbs-surface at a time, and hit Ctrl-A for opening the attribute editor.
-Under tesselation, set either U or V (or both, when needed) to...
well... try 3 or 4 or 5.
-A new render will clearly show the improvement.
-With "method" 2 you can set tesselation for several objects, and there is a funcion which sets "improved" tesselation for edges.
I usually use the attribute editor, but im still a newbie.
Hope this helps!
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