Why is the Trendelenburg position used when placing and removing Central Venous Line catheters in the sub-clavian vein?
There are 2 main reasons for using the Trendelenburg position when placing and removing a central venous line catheter into the subclavian or even internal jugular vein.


Exactly what C Rags mentioned-- to increase the size of the vein. This position utilizes the force of gravity to pool blood towards the head from the lower extremities. This makes the vein of interest easier to visualize compared to surrounding structures, to palpate since this increases pressure within the vein, and to ultimately puncture. 
To avoid air embolisms, which are particularly more damaging if they get into the brain causing a stroke than if they travel inferiorly to the leg, for example. Air embolisms can be introduced when inserting or removing a line. 


Ref:


http://emedicine.medscape.com/article/422189-overview#showall