./configure runs a script named "configure" in the current directory.
make runs the program "make" in your path, and
make install runs it again with the argument "install".
Generally, the "configure" script was generated by a collection of programs known as "autotools". It checks your system and tries to generate a makefile (see below) appropriate for your system. It often succeeds.
This makefile it creates (usually called "Makefile", note the capital "M") is used by the program make (on Linux it's probably GNU's make, but there are other versions) to actually compile the software.
make install command invokes make again, after the software is built, and tells it to execute the series of commands defined as "install" in the makefile.
These things are all conventional, so there's no guarantee that any random file named "configure" will actually do that, or that the target named "install" in a makefile will actually install software, but that's what most people expect from a file named "configure" in somebody's source directory: that it will generate a makefile to compile the program.