What are protecting groups in organic chemistry?
Functional groups become protecting groups out of practicality.

I would define an ideal protecting group (PG) as a functional group that is 


easy to introduce/attach to a given, other functional group (the protection target)
stable/non-reactive, i.e. protecting, under a wide range of reaction conditions
easy to remove by well-defined and mild reaction conditions 
with high yields throughout 


Clayden/Greeves/Warren/Wothers have referred to PGs as functional groups with an Achilles' Heel.[1] Obviously, the usefulness of a given PG is always dependent on the target molecule and the reactions it will undergo. The "easy" part of the definition also encompasses factors such as price and toxicity. 

As a corollary, one can introduce the concept of orthogonal PGs. Since the removal conditions can be very different for different PGs, one can successively attach PGs to, say, the hydroxyl groups of a sugar. By later removing them one by one, a chemist is then able to target them one at a time.[2]

Why do protecting groups tend to be large?

I am not convinced this is entirely the case, because I have seen applications of the methyl group as a PG. However, a larger group can introduce more steric hindrance or a point of attack for the removal that is different from the point of attachment to the protection target.



[1] Clayden, Greeves, Warren, Wothers: Organic Chemistry. Oxford University Press, 2004 (page 635).

[2] Werz, Seeberger, Angew. Chem. Int. Ed., 44, 6135, (2005). DOI:10.1002/anie.200502615.