This may consist of a raise, a promotion, change in title or job description, or a combination of these factors. It may even be just a promise of change to come. By buying you back, the company has bought itself some time, perhaps to finish that big project, reorganize other team members, or search for a suitable replacement for you. Because your company wants to attract you to stay, a counteroffer will usually come cloaked in flattery. Let's discuss this further before you make some rash decision.
Counteroffers can be tempting and ego-inflating.
You also may detect an underlying threat that by not accepting the counteroffer, you'll be throwing away your entire career, future, life. You have demonstrated your lack of loyalty by considering another opportunity. People will feel jilted, even if you accept a counteroffer and stay. Trust and acceptance among your immediate colleagues may be irrevocably lost. In any case, changes made as a result of a counteroffer may appease you in the short term, but rarely last for the long run.