Whats the use of Projected Sketch in Creo Parametric ?

yes i can understand you..you are using projected sketch and you are trying to extrude it . but it is not extruding. you want to know the use.. we can use projected sketch for sweep and swept blend where sketch is required on curved profile.

Project tool is extensively used for Surface modelling. In non-linear surfaces, the tool can be used to project a sketch on the surface. Then you can use tools viz. trim, offset.

First of all lol, creo is frustrating like that.
if you want to extrude a projected sketch you'll have to use the tool called "offset" (Model > Editing > offset) .
select the surface/ surfaces you want to extrude on, click offset,select first box drop down to the transparent box with light blue box coming out of it (3rd option), click options and under expand area select 'sketched region', define it using the define button that pops out, this is like the sketch for your projected sketch, once you accept the closed loop sketch your surfaces should turn amber, meaning it worked,if not make sure your sketch is not outside the selected surface. Unfortunately you can extrude till certain lengths due to solving issues, and i agree with your frustration about creo.