I have been through the answer of this question but do not quite understand the difference between system calls and library functions. Conceptually, what is the difference between the two?
Conceptually, a library function is part of your process.
At run-time, your executable code and the code of any libraries (such as libc.so) it depends on, get linked into a single process. So, when you call a function in such a library, it executes as part of your process, with the same resources and privileges. It's conceptually the same as calling a function you wrote yourself (with possible exceptions like PLT and/or trampoline functions, which you can look up if you care).
Conceptually, a system call is a special interface used to make a call from your code (which is generally unprivileged) to the kernel (which has the right to escalate privileges as necessary).
For example, see the Linux man brk.
When a C program calls
If there is already enough space for the allocation inside the process, it can do any necessary heap management and return the memory to the caller.
If not, glibc needs to request more memory from the kernel: it (probably) calls the
Adding to Useless' answer:
Syscalls on the other hand, since they run in the kernel, have access to everything in the system, and so they need to control what the calling process can do when it's calling them (verify that it has the permissions to open a file, for example), in addition, since syscalls are in the kernel, calling them requires a context switch in the CPU, which is a very heavy process relative to just calling a library call.
Syscalls usually reflect as system CPU usage in monitoring programs.