Please help ...What is meant by 'sparing' here in this context?

"Sparing" or "Sparingly" means "In small amounts" - not using something all in one go; rationing something out so it lasts a long time.

In that context, it means keep your opinions mostly to yourself rather than being overly vocal with them.

If one is sparing, it means s/he does not freely give an opinion, but does so to a limited extent.

Spare means to use as little as possible - from the idea that you kept thing back as spares against future need. 

"stingy"

I.e. don't give out many of those.

The wording is a little archaic, but it means, "Don't talk about yourself or your own personal opinions".. ie; make sure your comments are professional and business-like, not of a personal nature.