For use in the QGIS Python console

pyqgis_filter_vector_features.py

# Just the selected features
layer = iface.activeLayer()
for feature in layer.selectedFeatures():
    print feature['name']

# Filter by current extent of the map 
extent = iface.mapCanvas().extent()
request = QgsFeatureRequest()
request.setFilterRect(extent)
layer = iface.activeLayer()
for feature in layer.getFeatures(request):
    print feature['name']

# Filter by fixed extent
extent = QgsRectangle(-2.15, 52.20, 1.20, 52.60)
request = QgsFeatureRequest()
request.setFilterRect(extent)
layer = iface.activeLayer()
for feature in layer.getFeatures(request):
    print feature['name']

# Filter by attribute
exp = QgsExpression('name ILIKE \'%London%\'')
request = QgsFeatureRequest(exp)
layer = iface.activeLayer()
for feature in layer.getFeatures(request):
    print feature['name']