This is an old Irish proverb and as usual with these things, there is a lot of truth in it (pardon the pun)
Basically it means when you say something by accident and then try to cover it, there is usually truth in what you say.
For example, I could say to my friend "Yes, she's even bigger than you" (meaning someone is fatter than her) then I would realise my mistake and say something like "I mean she is a lot bigger than you, you are just right" but she would know that my real thoughts are that she really does need to lose weight.
Or you might talk at work about a great day out you had with the kids and then suddenly realise that you called in sick that day and try to cover it, they would have already realised that what you said when you weren't being guarded with what you said was actually the truth.