What are Non-deductible Contributions

There are so many taxed terms that confused me.

As I understand that ROTH IRA is where you put your after-tax contribution with future distribution taxed free and Tradition IRA or 457 IRA is where you put your pre-tax contributions and are subjected to taxes on the distributions.

Then, there is the words ”non-deductible contribution”, what does that “non-deductible” applies with regard to your income?  In a W2 form, we have Wages and Medicare wages and also C, G and DD on lines 12a, 12b and 12c respectively. Isn’t what is non or deductible already taken care?  So,  is pre-tax contribution deductible?

Also, Investopedia Website says:

Basically, you must file Form 8606 for every year you contribute after-tax amounts (non-deductible contributions) to you Traditional IRA.

Is there an IRA that you contributed with your after-tax dollars? If so, what is the advantages consider that you can simply open an investment account with your after-tax dollars and why have IRA come into play? Please advise.