gcc is a C compiler: it takes a C source file and creates machine code, either in the form of unlinked object files or as an actual executable program, which has been linked to all object modules and libraries.
make is useful for controlling the build process of a project. A typical C program consists of several modules (.c) and header files (.h). It would be time-consuming to always compile everything after you change anything, so make is designed to only compile the parts that need to be re-compiled after a change.
It does this by following rules created by the programmer. For example:
foo.o: foo.c foo.h
cc -c foo.c
This rule tells make that the file foo.o depends on the files foo.c and foo.h, and if either of them changes, it can be built by running the command on the second line. (The above is not actual syntax: make wants the commands indented by a TAB characters, which I can't do in this editing mode. Imagine it's there, though.)
make reads its rules from a file that is usually called a Makefile. Since these files are (traditionally) written by hand, make has a lot of magic to let you shorten the rules. For example, it knows that a foo.o can be built from a foo.c, and it knows what the command to do so is. Thus, the above rule could be shortened to this:
foo.o: foo.h
A small program consisting of three modules might have a Makefile like this:
mycmd: main.o foo.o bar.o
$(CC) $(LDFLAGS) -o mycmd main.o foo.o bar.o
foo.o: foo.h bar.h
bar.o: bar.h
make can do more than just compile programs. A typical Makefile will have a rule to clean out unwanted files:
clean:
rm -f *.o core myapp
Another rule might run tests:
check: myapp
./myapp < test.input > test.output
diff -u test.correct test.output
A Makefile might "build" documentation: run a tool to convert documentation from some markup language to HTML and PDF, for example.
A Makefile might have an install rule to copy the binary program it builds to wherever the user or system administrator wants it installed.
And so on. Since make is generic and powerful, it is typically used to automate the whole process from unpacking a source tarball to the point where the software is ready to be used by the user.
There is a whole lot of to learn about make if you want to learn it fully. The GNU version of make has particularly good documentation: http://www.gnu.org/software/make/manual/ has it in various forms.