What is makefile and when do I need to use it along with latexmk?

This is a quite general question, and so it'll be hard to write down a complete answer. I'll talk about when I use Make and when I use latexmk.

latexmk is a tool for compiling .tex files, and not much else. However, it's good at determining which files depend on which other files: you don't need to provide a list, so latexmk main will only recompile when a dependency of main.tex has changed. latexmk will also compile files two or three times if needed (e.g. for bibliography, index, or hyperlink updates).

Make is much more general, but requires an explicit description of a file's dependencies and how to compile it. This information is provided in a file usually called makefile. Suppose main depends on main.tex, macros.tex, and eggs.tex, and that it sometimes needs to be compiled twice. Then, the makefile might like this:

# example makefile

INPUTS = main.tex macros.tex eggs.tex
COMPILER = pdflatex --halt-on-error

main.pdf: $(INPUTS)
    $(COMPILER) main.tex
    $(COMPILER) main.tex

It's more work to manually specify the dependencies and compilation instructions, especially since they can change throughout a project. But Make's advantage is that it can execute any command. If your final file depends on running some statistical test and including the results in your document, Make can run the test. If your file contains code listings, latexmk doesn't know to watch them for changes, but you can update $(INPUTS) to include them if you're using Make.

Another use for Make is to automatically do something to your output files after compilation.

In summary, Make is more complicated, but able to handle non-TeX dependencies, so use it only if you have non-TeX dependencies or need to do postprocessing.

Examples of such dependencies:

• source code listings in a non-TeX language
• statistical graphs or statistical analyses that are automatically generated from data
• images that are automatically generated from inputs or data
• information obtained from the “outside world,” e.g. the user or the Internet

Examples of postprocessing:

• Converting the output PDF into an image
• Moving the output PDF into another directory
• Compressing the output PDF

I would like to know what makefile is

The command make most often refers to GNU make or BSD make. Each variant has its merits; the differences are for advanced uses not discussed here. Regardless of which variant is used, make expects to find a file named Makefile which contains recipes on what files (so-called targets) to build from other files (so-called dependencies) and what commands to use for building the targets. make then figures out what targets need to be built or rebuilt and issues the required commands. Essential points:

• You have to write a Makefile with the needed recipes.
• make executes each rebuild command for a given target at most once. That is unfortunate for LaTeX document processing where e.g. several pdflatex runs may be needed.
• make detects changes in dependencies by looking at file last-written times. But every pdflatex run writes an .aux file, therefore the next make run will behave as if the .aux file had changed, regardless of whether its actual contents have changed or not.

So if you'd like to formulate a recipe that re-runs pdflatex until .aux file contents do not change anymore, this is not a straightforward thing to do with make. With a lot of sophistication and some tricks, it is possible to formulate a useful Makefile, but its recipes tend to look very complicated.

latexmk is specialized for LaTeX-based document processing. It knows how to employ the various *tex programs and auxiliary tools like bibtex, biber, or makeindex. It does not need a Makefile, it can repeat commands as needed, and it detects changes by looking at file contents (actually checksums) rather than last-written times.

when I need to use both makefile and latexmk instead of latexmk only

There is an answer proposing a Makefile fragment that causes make to do the equivalent of latexmk -pdf. In fact, such a make will delegate the document processing details to latexmk -pdf with some fancy options added. So why use make at all then?

If you just want the functionality of latexmk, you do not need make. However,

• You can add more recipes to the Makefile so that make can do more things than just processing LaTeX documents. Cf. Arun's answer. I typically add recipes for compiling programs, running tests, producing illustrations, and the like.
• Users of open-source software universally expect that make will build the files they want. By providing a suitable Makefile, this expectation is met.
• make is shorter to type. If you recompile frequently, such things matter.

If the above reasons do not appeal to you, you might sum those up as:

make with latexmk is for users already accustomed to make who recognize the utility of latexmk.