What are solvolytic displacement reactions?
A book could be written on this subject!

A solvolysis reaction is an $\ce{S_{N}1}$ reaction where the solvent acts as the nucleophile and replaces the leaving group.  The following reaction is a solvolysis reaction run in ethanol.



I suspect there are some industrial uses of solvolysis reactions and they have been used in labs and by drug companies as a step in a synthetic sequence to prepare some complex molecules.

But I suspect the biggest contribution from the study of solvolysis reactions is the impact they have had on our understanding of carbocation chemistry.  From our study of solvolysis reactions we have learned how and why some carbocations rearrange before being captured by solvent.



While studying such rearrangements the solvolysis of the norbornyl system was examined.  



It turns out that 


norbornyl compound 1 solvolyzes several hundred times faster than compound 3 - why?
if compound 1 is prepared optically active, the products are racemic - why?
If compound 1 is radiolabeled, the label is scrambled in the products - why


It took decades to answer these and other questions.

These investigations led to a whole new field of carbocation chemistry: the classical - non-classical carbocation debate (see the norbornyl link above for a discussion of this topic).  These investigations added a whole new section to physical organic chemistry textbooks.  What was learned from these solvolysis studies completely changed our thinking about carbocation chemistry.