I understand why you'd need to declare other things, but I'm not sure why money should be investigated. Why do countries have such laws in place?
This requirement is usually in place to combat money laundering and tax evasion. The Financial Action Task Force on Money Laundering, an international organization, has a series of recommendations for countries to fight money laundering, including Recommendation 32—"Cash Couriers":
Countries should have measures in place to detect the physical cross-border transportation of currency an d bearer negotiable instruments, including through a declaration system and/or disclosure system. Countries should ensure that their competent authorities have the legal authority to stop or restrain currency or bearer negotiable instruments that are suspected to be related to terrorist financing, money laundering or predicate offences, or that are falsely declared or disclosed.
While there are legitimate reasons to carry large amounts of cash across international borders (the limit for what can be carried without a declaration varies from country-to-country), there are plenty of illegitimate reasons. With the increasing availability of low-cost international transfers, the reasons to carry that much cash are increasingly few.
Requiring a declaration means the country has records of what cash is coming in and out, records that can be searched to look for suspicious behavior. And anybody who fails to declare cash is inherently going to be under suspicion. In this way, currency declaration laws create a "predicate crime," where the authorities can investigate and prosecute the failure to declare without having to prove another offense or an illegal use for the funds.
Border crossings are often used in money laundering. Sure, you could be doing it with $100, but it's probably not worth your while. They have to set a point at which it warrants more investigation. That's a handy round figure that is more than most people will bring in for a holiday, is easy to calculate if you're above or below (usually), and stands out visually.
From Australia's forms:
Cross-border movements of AUD10,000 or more of physical currency (or the equivalent in foreign physical currency) must be reported to AUSTRAC under the Anti-Money Laundering and Counter-Terrorism Financing Act 2006 (AML/CTF Act).
Just to be clear, there are no limits to the maximum amount of currency you can carry across the border (in either direction, while entering or exiting a country).
The only requirement is:
Any amount above USD 10,000 (or equivalent) must be declared; and you must show proof of where you got the funds.
If the source of funds cannot be determined to be legitimate; then you may be suspected of money laundering.
Money laundering is not related to funding terrorism, although the two are often conflated these days.
Laundering of funds has been around as long as there has been illegitimate businesses.
However, a large majority of money is laundered specifically for the financing of (or as proceeds of) terrorism; which is why they are now linked.