What are the origins and original purposes of searches and seizures?
Lets look at what "search and seizure" means. The "search" part reflects the interest of an authority (usually law enforcement) in searching a person or corporation's belongings for evidence of illegal activity. The "seizure" part is the confiscation of what is found that is deemed illegal (or gives evidence of illegal activity.)
From this context, the first part of your question is harder to answer. As long as there have been authority figures there have been searches of property. I am thinking back to the old testament story of Rachel taking her family's "house gods" and Laban searching the tents for them. My point is, as long as there have been people in charge of others, searches have been going on.
As for the seizure part, the authority figures are generally looking for either contraband or evidence of other crimes. In the United States, much of the early searching in this context would have been for smuggled goods or signs of tax evasion to avoid British taxation. Stolen goods would likely have been a close second in terms of prompting a search. In other parts of the world, evidence of political dissent, subversion, or terrorist activity are also likely candidates for the seizure of property. In some cases, it is possible to sieze a person's property for practicing an upopular religion or holding unpopular political beliefs.
This concept of "search and seizure" was a big one in the American Revolution. The colonists didn't like the fact that their homes and warehouses could be entered on even the suspicion (i.e., someone's guess) that they had contraband.
The fourth amendment to our Constitution was put in place to restrict the government's ability to search and take a citizen's property in order to address just such Revolutionary-era abuses.