ABI - Application Binary Interface
"ABI" describes the low-level interface between an application program and a library. Calling conventions, function arguments, return values, struct sizes/defines and more.
In the vast majority of all cases, a typical libcurl upgrade does not break the ABI at all. Your application can remain using libcurl just as before, only with less bugs and possibly with added new features. You need to read the release notes, and if they mention an ABI break/soname bump, you may have to verify that your application still builds fine and uses libcurl as it now is defined to work.
In libcurl land, you really can't tell by the libcurl version number if that libcurl is binary compatible or not with another libcurl version.
Whenever there are changes done to the library that will cause an ABI breakage, that may require your application to get attention or possibly be changed to adhere to new things, we will bump the soname. Then the library will get a different output name and thus can in fact be installed in parallel with an older installed lib (on most systems). Thus, old applications built against the previous ABI version will remain working and using the older lib, while newer applications build and use the newer one.
During the first seven years of libcurl releases, there have only been four ABI breakages.
We are determined to bump the SONAME as rarely as possible. Ideally, we never do it again.
Going to an older libcurl version from one you're currently using can be a tricky thing. Mostly we add features and options to newer libcurls as that won't break ABI or hamper existing applications. This has the implication that going backwards may get you in a situation where you pick a libcurl that doesn't support the options your application needs. Or possibly you even downgrade so far so you cross an ABI break border and thus a different soname, and then your application may need to adapt to the modified ABI.
The previous major library soname number bumps (breaking backwards compatibility) have happened the following times:
0 - libcurl 7.1, August 2000
1 - libcurl 7.5 December 2000
2 - libcurl 7.7 March 2001
3 - libcurl 7.12.0 June 2004
4 - libcurl 7.16.0 October 2006