Having secrets between you and your partner sounds like a not very good thing to do. Divorce and the challenges of life after divorce might not be far away. But no, it could be just the thing to do.
Trusting your partner is not the same as sharing everything in your life and in your past. It means loving, honoring and respecting your partner and sharing what can be shared whilst trusting that what is not shared is no threat or challenge to the relationship.
Marriage is not a fusion of two people into one but an intimate and total collaboration between two people which allows each to maintain their individuality and sense of uniqueness.
What are these private aspects of life that remain unshared? They are different for men and women and probably far more common in men than women. It's all part of the men are from Mars and women from Venus stuff. The best advice is to treat these unshared elements of your partner's life as part of his/her individuality and a positive element of the relationship. However that advice would be different if the secrets were to do with criminal behaviour, illness or some other important issue.
All men look at and admire attractive women all the time
There is nothing unnatural in a man looking at and admiring other women as long as it's done in a discreet way and does not embarrass the women being admired or his partner by his side. It's not that he does not find his partner attractive; it's just that it doesn't stop him appreciating other women too. It's no reason to see life after divorce lurking just around the corner.
All men have a past and sometimes lots of it
Men are unhappy about revealing much of the detail of their past relationships. This is often because they are not that proud of how they handled things. This should not be seen as threatening by their partner. The only exception to this is if there has been a history of unacceptable behaviour especially domestic violence. Unfortunately this is more common than we might believe and few men have come to terms with it enough to tell their partner. This is a common reason for a divorce.
All men want a bit of space with other men, this usually involves extreme sports and/or drinking
No surprise here. Whether it's a game of bowls (that's the one played on the immaculate lawn and everybody wears white) or skiing down a Tibetan mountain men like some time to do that stuff. Women should not be threatened by this; much of what happens on these male bonding occasions remains unreported to spouses. Not because anything really happened at all but it's just men's stuff.
Women need secrets too
Women pretty much do the same thing but in a different context. It's a bit of a cliché (well an awful lot of a cliché actually) but a highly trained group of women making a frontal assault on a department store and ravaging their way from Perfume to Garden Furniture via Designer Clothing can make Himalayan downhill skiing look like a walk in the park.