Hi bartosh, here's one example. Here are 7 coplanar curves:
You can take these curves and construct one surface from them using Construct > Planar, which gives this result:
That's a trimmed surface  if you select it and turn on surface control points you'll see the control points for the "underlying surface" are just 4 corner points making a simple plane:
There is also the concept of an "untrimmed surface"  that's a surface that doesn't have any additional trim curves on it other than the underlying surface's own boundaries. Often times the process of construction will involve building some untrimmed surfaces to start with like with sweep, loft, extrude, or whatever, and then doing boolean operations on them which then introduces new trim curves. This concept of building an initial simplified extended piece of "stock material" which then gets cut by some boolean operations is pretty central to NURBS modeling. So booleans are usually the main way to do things in NURBS modeling, which is a very different strategy from subd modeling where you've learned to avoid booleans entirely. There are some tips here for people coming from a poly modeling background which may be useful: http://moi3d.com/forum/index.php?webtag=MOI&msg=4865.2 . One of the key things is that you don't start by drawing in all the 3D edge curves that make up your model, instead you should mostly be working with 2D curves and generating solids from some 2D curves by extrusions for example, and then use other 2D curves or other solids to cut away portions. So some of the final edges in the 3D model are not ones that you draw directly, they're trim curves that are the result of intersection and cutting operations.
The NURBS strategy of "build a sheet of stock material and then cut it with booleans" tends to work well with real world manufacturing processes and so it's a very good strategy to use for mechanical man made type parts.
This concept of having an "underlying surface" and then trim edges that live on that surface is why booleans work much much better in NURBS modeling than they do in polygon modeling. In NURBS modeling when 2 solids are booleaned together, it only involves the creation of new trim curves, the "underlying surfaces" of each surface remain the same, they aren't fragmented into tons more little tiny pieces like will happen when doing poly modeling booleans.
Also you can recover the full "underlying surface" that is part of a trimmed face by selecting all the edges of a single trimmed surface that is not joined to anything else and using Delete.
 Michael
