Valgrind is a suite of tools for debugging and profiling C and C++ programs. Memcheck is its most popular tool for detecting memory errors like leaks, accesses to uninitialized memory, and invalid reads/writes. It works by instrumenting the program binary to track "V-bits" and "A-bits" associated with each value and memory location. When the program is executed, Memcheck checks these bits to detect errors and produces detailed error reports with stack traces. The tutorial provides instructions on running Memcheck, understanding its output, and using options like suppressions and attaching a debugger. It also briefly describes how Memcheck works and lists some other Valgrind tools.