Retirement tax questions

Let me ask you one more question.  I was told that contributing money to a traditional IRA from say a checking account will eventually lead to me being double taxed.  Money in my checking account already had taxes taken out primarily because they were from past paychecks.  If I put this money into an IRA I will have to pay taxes again on what I withdraw.  Will the savings I get on my 2019 return more than offset this so called double taxation?