Static meshes (sometimes called hardware brushes) or shortly (s)meshes - are 3D models that can be used in your level to introduce additional details on top of BSP, finish geometry of your level or decorate it. Static meshes are generally much more detailed (applies even more for UT3) than your brushwork (that should be as simple as possible!). You can use static meshes delivered with UT3, take some from other maps (with author's permission of course) or model them on your own in some modeling application (Maya, 3DS Max, Blender).
Geometry of static meshes is cashed on your video card and multiple instances of the same mesh don't stress the hardware as would do the same geometry via BSP. Today's graphics accelerators can process (transform) static meshes very fast not to mention that cashing means lower GFX memory consumption. BSP is generally not optimal for detailed modeling and it's also error prone while static meshes don't have any of these weaknesses.
Static Mesh Catalog - list of UT3 stock packages containing static meshes with keywords to ease your searching + pictures of all static meshes
Static Mesh Editor User Guide on UDN beta
Importing Static Mesh Tutorial on UDN beta
Tutorial on exporting SM from Blender by IronMonkey - hosted by IceCreamYou
Anything that relates to UT2004 (that means UnrealEd 3) is hardly usable in UnrealEd for UT3 - but you might want to check it anyway. You can find there some general modeling procedures that might be useful. So here it goes:
UnrealWiki references: Static Mesh and SM modeling - applies mostly to UT2004 version
Static Meshes on UDN - again for UT2004 Editor
Static Mesh on Wikipedia - looks like the guys from UnrealWiki wrote this ;-)