Is it a good practice to place C++ definitions in header files?
Your coworker is wrong, the common way is and always has been to put code in .cpp files (or whatever extension you like) and declarations in headers.
There is occasionally some merit to putting code in the header, this can allow more clever inlining by the compiler. But at the same time, it can destroy your compile times since all code has to be processed every time it is included by the compiler.
Finally, it is often annoying to have circular object relationships (sometimes desired) when all the code is the headers.
Bottom line, you were right, he is wrong.
EDIT: I have been thinking about your question. There is one case where what he says is true. templates. Many newer "modern" libraries such as boost make heavy use of templates and often are "header only." However, this should only be done when dealing with templates as it is the only way to do it when dealing with them.
EDIT: Some people would like a little more clarification, here's some thoughts on the downsides to writing "header only" code:
If you search around, you will see quite a lot of people trying to find a way to reduce compile times when dealing with boost. For example: How to reduce compilation times with Boost Asio, which is seeing a 14s compile of a single 1K file with boost included. 14s may not seem to be "exploding", but it is certainly a lot longer than typical and can add up quite quickly when dealing with a large project. Header only libraries do affect compile times in a quite measurable way. We just tolerate it because boost is so useful.
Additionally, there are many things which cannot be done in headers only (even boost has libraries you need to link to for certain parts such as threads, filesystem, etc). A Primary example is that you cannot have simple global objects in header only libs (unless you resort to the abomination that is a singleton) as you will run into multiple definition errors. NOTE: C++17's inline variables will make this particular example doable in the future.
As a final point, when using boost as an example of header only code, a huge detail often gets missed.
Boost is library, not user level code. so it doesn't change that often. In user code, if you put everything in headers, every little change will cause you to have to recompile the entire project. That's a monumental waste of time (and is not the case for libraries that don't change from compile to compile). When you split things between header/source and better yet, use forward declarations to reduce includes, you can save hours of recompiling when added up across a day.
What might be informing you coworker is a notion that most C++ code should be templated to allow for maximum usability. And if it's templated, then everything will need to be in a header file, so that client code can see it and instantiate it. If it's good enough for Boost and the STL, it's good enough for us.
I don't agree with this point of view, but it may be where it's coming from.
Code in headers is generally a bad idea since it forces recompilation of all files that includes the header when you change the actual code rather than the declarations. It will also slow down compilation since you'll need to parse the code in every file that includes the header.
A reason to have code in header files is that it's generally needed for the keyword inline to work properly and when using templates that's being instanced in other cpp files.
The day C++ coders agree on The Way, lambs will lie down with lions, Palestinians will embrace Israelis, and cats and dogs will be allowed to marry.
The separation between .h and .cpp files is mostly arbitrary at this point, a vestige of compiler optimizations long past. To my eye, declarations belong in the header and definitions belong in the implementation file. But, that's just habit, not religion.