What does it mean by the saying "The truth will set you free"?

It means that telling lies weigh us down, and that when we tell lies, we are caught in a web of deceit, and weighed down with the burden of remembering and maintaining our lies. None of that happens when we tell the truth.
It can also mean that not KNOWING the truth can weigh us down. Knowing the truth, however awful, is better than not knowing, and is better than being told lies.

If you tell a lie then you have to keep making up stuff to support that lie. after a while the amount of stuff you have to remember to keep the lie going is so much that you are stressed out.

If you do not lie..or if you come out and tell the truth you will be free of stress.

BUT - if the lie was to your friend that 'Yes - you like her new boyfriend' ..but you don't and he proposes to her and she is all happy...you NEVER EVER say: Ewwww...you know I lied to you and I really don't like him at all!!!'

.....because you will lose a friend.

I understand it in the context of keeping a lie. If you just tell the truth vs perpetuating a lie than you will be free of any guilt or other issues you may be experiencing.

For those whose lies make them feel guilty, the truth will set them free.

"What does it mean by the saying" makes no sense.

You mean "What does the saying 'The truth will make you free' mean?"

You Will Know the Truth and the Truth Will Set You Free

https://www.desiringgod.org/messages/you-will-know-the-truth-and-the-truth-will-set-you-free

"The truth will set you free" means that by telling the truth about an issue will release you from the guilt associated with the issue.