http://www.allaboutcircuits.com/vol_4/chpt_12/3.html

The SN74LS674 and an SC input. Does anyone know exactly what this input does?

 

hi,
Do you mean pin#1 , which is /CS.?
If so, its Low to Select the IC.
E
Which pin number is it on the 24pin DIL package.?

 

So pulling it high will disable the clock, deselecting the IC?

 

Setting /CS High will disable the IC.
Sometimes more than one Shift Reg can share the same Clock and Data lines, so the /CS is used to select the required S/R.