Strace is a system call tracer, i.e. a debugging tool which prints out a trace of all the system calls made by a another process/program. The program to be traced need not be recompiled for this, so you can use it on binaries for which you don't have source.
System calls and signals are events that happen at the user/kernel interface. A close examination of this boundary is very useful for bug isolation, sanity checking and attempting to capture race conditions.