Doldis is used to talk about someone who is not a household name and is usually not especially publicity-seeking.
It's not as unkind or dismissive as saying someone is 'a nobody' in English, and in fact you use it in a different way. A doldis is rarely an average member of society, but someone who has a high status or level of influence, such as an important job or rank, but is not yet one of the biggest names in their field.
So it might refer to a player in a football team, but not one of the club's big stars. It could be an athlete who competes internationally, but is ranked outside the world's top 20 in their sport and doesn't have much of a fan following. Or it could be a politician or businessperson who is close to the top in their field, but few people outside it have heard of them.
Doldis comes from adding the popular Swedish suffix 'is' to the adjective dold (hidden) to turn it into a noun.
Sweden has two words meaning 'to conceal': dölja (from which we get dold) and gömma. Gömma and the adjective gömd usually refer to something that has actively and deliberately been hidden from view, whereas dölja and dold are mostly used when the hiding could be accidental, for example if something is concealed from view simply because something else is in the way. This distinction can help you understand what makes someone a doldis: they haven't necessarily avoided the limelight on purpose, they've just not reached it, perhaps because others in their field are better-known or more publicity savvy.
The opposite to doldis is kändis, which refers to someone well known: en känd person means 'a well-known person', so kändis is a snappy way to say 'celebrity'. You're likely to hear the word kändis much more often than doldis because, well, people tend to talk about well-known people far more than they talk about little-known people.
When you do hear the word doldis, ironically it tends to be because these lesser-known people have done something that suddenly marks them out.
For example, when Prime Minister Stefan Löfven named his government ministers on Monday, several newspapers wrote that the new cabinet included flera doldisar (several little-known people).
Sports is another context where it may come up, particularly when a low-ranking team or player suddenly perform unexpectedly well. 'Doldis låg bakom seger' (unknown player behind victory) one headline might read, or 'doldis blev matchhjälte' (unknown player became hero of the match).
This is because it creates a more exciting narrative that grabs reader's interests – who is this mysterious hero who's come from nowhere to steal the match? – than if the headline includes a name most readers wouldn't recognize. But by the time someone is openly described as a doldis, it's usually because their star has already begun to rise.
Flera doldisar har blivit ministrar
Several little-known people have become ministers
Doldis tar över på Ikea
An unknown person takes over the reins at Ikea (a Dagens Industri headline)