Is it possible to extract a small portion of data from an entire database? If possible then how can I do it. I want data to be extracted which is within my map view only, so that other data objects are excluded: only objects contained in the map view should be in the extract.
As with your other question, you've failed to specify which database you're using and the SQL will vary a bit between databases. I'll leave others to deal with this aspect.
Given you're apparently using FME (per your other question), you can use that to do it in a couple of ways:
a) Once you've added the reader you can specify Maximum x,y and minimum x,y as parameters and the reader will only select features within those bounds. That creates a square bounding box.
b) Alternately you can pass the data through a SpatialFilter and check against a shape of your given area. Use the "INTERSECTS" test.