(Dai wa shou wo kaneru; “The large does the work of the small”)
Something that is more can do the work of something that is less. Better too much than too little. It is possible to use a large tool in place of a small tool, but not vice-versa. So for example, you can cut a grape with a huge chef’s knife, but not a watermelon with a tiny paring knife. Or at least, one of those imbalances is less inconvenient than the other.
大 (dai) is technically not a normal part of speech; my prime dictionary categorizes it as a “prefix.” In this case, both it and 小 (shou) are clearly operating, grammatically, as nouns. Dai is “big,” in this case rendered by sense as “the large,” while shou is “the small.” The first noun is followed by the topic-marker は (wa); meaning the saying is primarily about “the large.” The latter noun is marked as an object by the particle を (wo), and the verb that acts upon it is 兼ねる (kaneru). This is a fascinating verb that can have some pretty divergent meanings depending on the exact context of usage, but here means “to serve multiple functions simultaneously.”
A clunky but sense-literal rendition of the phrase would give us something like “As for big things, they also do the work of small things.”
There are some pretty obvious situations where this isn’t true, of course. I’d rather have a too-small cooking fire than a too-big one, probably. Too little anesthesia in a given dose rather than too much. But in many practical situations, it is indeed better to have more of a given resource than too little.
This saying is based on a passage in The Luxuriant Dew of the Spring and Autumn Annals (春秋繁露), a 4th-century (or so) Neo-Confucian text.
An alternate version of this saying replaces the final verb with 叶える (kanaeru, “to fulfill [a desire/condition/requirement]”). Note how close the verbs are phonetically.
(“Hondana ni narandeita jiten wa minna buatsukute, gokiro wo koeru hon mo takusan atta. Tarou no otousan wa, ‘Dai wa shou wo kaneru‘ to shinjiteita no darou.”)
[“The dictionaries lining the bookshelf were all thick tomes; many were over five kilograms in weight. Taro’s father seemed to have believed that ‘The greater serves for the lesser.’”]