That would usually mean she didn't let out the secret. He still doesn't know the secret.What does it mean by "She almost told him a secret."?
Does it mean that she told him a part of the secret but not all of the secret or she did not tell him a secret after all?
That would usually mean she didn't let out the secret. He still doesn't know the secret.
However, context plays a role as usual.
"She talked to him for hours and told him all about her unhappy childhood and her drunken father. She almost told him the secret of why she couldn't commit to a relationship."
In this case, it could mean that she told him part of the secret, or made the information a bit less secret.