Ask Dad! He knows

What does mysterious things mean? Is it some products you valued as curious and mysterious things as a boy? As you were too young to recognize what it is?
What does unknown world mean? Unknown world for children as children are so unware of the world?

ex)Words are as frequently used as stimuli to action. A familiar instance is seen in the use of words in advertisements. Even the honest advertiser is less interested in giving an analysis of his product that will win him the rational estimation and favor of the reader than in creating in the reader through the skillful of words, emotions and sympathies favorable to his product. The name of a talcum powder or tabacco is the subject of mature consideration by the advertising expert, because he knows that the emotional flavor of a word is more important in securing action than its rational significance.
"Ask Dad! He knows!" does not tell us much about the article it advertises, but it gives us the sense of secure trust that we had as a boy in those mysterious things in an almost completely unknown world which our fathers knew and approved.

"mysterious things" here means things that we could not fully understand when we were children; for example, a child hearing his parents talk could now and then stumble upon something that was still hard for him to grasp, but was a somewhat frequent subject in their conversations. A father could tell his son not to put too much butter on a piece of bread "'cause it clogs up your heart". These little things constituted the "unknown world" in the mind of the child. It was something his little mind was yet to start comprehending.

Bennevis said:

"mysterious things" here means things that could not fully understand when we were children; for example, a child hearing his parents talk could now and then stumble upon something that was still hard for him to grasp, but was a somewhat frequent subject in their conversations. A father could tell his son not to put too much butter on a piece of bread "'cause it clogs up your heart". These little things constituted the "unknown world" in the mind of the child. It was something his little mind was yet to start comprehending.

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Then, how does it affect the influence of advertisements quoting such childhood memories?

It affects the viewer on an emotional level.

The title of this post reminded me of the story of the boy doing his homework on the floor as his father was reading his newspaper. The boy said, "Dad, where are the Alps?" His father was not paying attention and replied, "I dunno- ask your mother. She puts everything away..."

keannu said:

Then, how does it affect the influence of advertisements quoting such childhood memories?

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If, say, the product is used by older people, then the tagline 'Ask Dad! He knows' could suggest to younger people that this is a product they can trust.