Spick and span
Entirely new - fresh or unused.
The noun spick has various meanings, or rather it had various meanings, as it is now rarely used outside of spick and span. These include: a side of bacon, a floret of lavender, a nail or spike, a thatching spar.
Likewise span has/had several meanings, including: the distance from the tip of the thumb to the tip of the little finger, a measure of butter, a fetter or chain, a chip of wood (as the Norse word spann-nyr).
Just from those meanings, and there are more, we could generate sixteen possible combinations to form spick and span. It isn't clear which, if any, of those words were used when coining the phrase. Some clue might come from the fact that the phrase is very old and was originally spick and span-new. This is cited in Sir Thomas North's translation of Plutarch's Lives of the noble Grecians and Romanes, 1579:
"They were all in goodly gilt armours, and brave purple cassocks apon them, spicke, and spanne newe."
The alliteration in the phrase suggests the possibility that that one of the two words alluded to cleanliness and freshness and that the other just followed along. Which one is most associated with the qualities of spick and span? The suggestions most frequently made are that spick is a variant of spike or nail. In the 16th century nails were made of iron and soon tarnished. It is quite plausible that new nails would have become synonymous with cleanliness. We have the phrase as neat as a new pin, which has just that meaning. The old Dutch word spikspeldernieuw refers to newly made ships. The OED suggests that this is the origin of spick, although they offer no reason for that belief and none of the early citations of the phrase refer to shipping. As for span, chips of wood also display the same fresh, sharp-edged qualities and seem to be a plausible source for the use of the word here.
Note: the word spoon, which was originally a wooden item, derives from spon - a variant of span. It has been suggested that the early American term for a knife and fork was spike and spon and that this relates to keeping clean by using utensils rather than fingers. That takes no account of the use of the phrase prior to the colonization of America by English-speaking people though.
Spicke, and spanne newe later migrated into simply spick and span which is first found in Samuel Pepys' Diary, 1665:
"My Lady Batten walking through the dirty lane with new spicke and span white shoes."
All in all, the derivation of the term isn't clear and our best efforts to explain it so far are little more than informed guesses.
Many American readers will know Spic and Span as the cleaning product marketed by Prestige Brands Inc. This has the strapline 'The Complete Home Cleaner', so, next time you want to clean a complete home you know what to use.
The use of spic in that product name is just an alternative spelling of spick. This has no connection to spic as used for the offensive term for Spanish-speaking American residents, also called spiggoties or spigs. That term originated in the early 20th-century and is cited in Harry Franck's Zone Policeman, 1913:
"It was my first entrance into the land of the panameños, technically known on the Zone as 'Spigoties', and familiarly, with a tinge of despite, as 'Spigs'."