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Let's disregard vestments (clothing) for a moment and consider hats. In many cultures, specific hats are associated with different social roles. Sometimes these are strictly regulated by sumptuary laws, and sometimes they are on a spectrum between mandatory and fashionable. E.g. a firefighter's helmet, a police officer's hat, a soldier's cover -- these are partially functional but also convey social meaning. We literally refer to US Army Special Forces as "green berets". A person wearing a different hat embodies a different social role, and will act and be expected to act in different ways.

When we "invest" in non-financial senses, we put something into a different role. We invest a person with the power of an office; we invest our selves into a set of beliefs. We take the thing and give it a different hat, and while it is wearing the hat, we expect it to be different.

So, financially, we invest money, time and effort into businesses and expect that to act differently from the money, time and effort we have not so invested.