QGIS uses GEOS to properly fetch features from the database when doing an identify or select. You can still view PostGIS layers without GEOS, but you will not be able to create a selection or identify a feature.
If you choose to proceed without GEOS support, QGIS will warn you each time you load a layer from the database.
To install GEOS:
tar -xzf geos-1.0.0.tar.gz
cd geos-1.0-.0
./configure make make install