Sayur (or the often still used old Dutch spelling sajoer) is a food item from Indonesia that is hard to translate in English (or other western languages for that matter).
The best translation is possibly simply vegetable soup, but that does not entirely cover the term. In a number of sayurs meat is included in the recipe, so it's not vegetable soup, per se.
The trouble with this term probably stems from the fact that Indonesian food traditions differ from regular western food traditions. In the west, soup is usually eaten as an appetizer1, while sayur is part of the main course. In fact, in Indonesian cuisine there is no such thing as an appetizer or a main course. There is just the meal itself2.
Also, sayur is usually the healthy part of a meal, so instead of a vegetable side dish, sayur is served. The sayur is also there to provide some moisture for the rice, which is the main ingredient - the staple - of an Indonesian meal. Of course, it is very possible to have a meal that includes a meat dish that is not entirely dry, but when it consists of dry ayam goreng it is often nice to have some sayur lodeh or sayur bayam to moisten it all up a bit.
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1 Or at a Sunday brunch with some french bread or something like that.
2 Although now I start to wonder, as in western countries it is not the normal state of things to eat an appetizer with every meal one partakes in, right?
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Sources:
Groot Indonesisch kookboek (Large Indonesian cookbook) by Beb Vuyk.