What is the purpose of using -pedantic in the GCC/G++ compiler?

This note says:

-ansi: tells the compiler to implement the ANSI language option. This turns off certain "features" of GCC which are incompatible with the ANSI standard.

-pedantic: used in conjunction with -ansi, this tells the compiler to be adhere strictly to the ANSI standard, rejecting any code which is not compliant.

First things first:

• What is the purpose of the -pedantic and -ansi options of the GCC/G++ compiler (I couldn't understand the above description)?
• What are the right circumstances for using these two options?
• When should I use them?
• Are they important?

GCC compilers always try to compile your program if this is at all possible. However, in some cases, the C and C++ standards specify that certain extensions are forbidden. Conforming compilers such as GCC or g++ must issue a diagnostic when these extensions are encountered.

For example, the GCC compiler’s -pedantic option causes GCC to issue warnings in such cases. Using the stricter -pedantic-errors option converts such diagnostic warnings into errors that will cause compilation to fail at such points. Only those non-ISO constructs that are required to be flagged by a conforming compiler will generate warnings or errors.