What type of strategy game is this? You rearrange positions

It's not a definition set in stone - but it usually refers to a game published by a major publisher, enjoying a large budget (can be millions of dollars) and a large team working on it over a few years. AAA titles typically also have a lot of publicity.

The term does not say anything about the game quality or sales figure.

It's a genre where the primary form of gameplay is to locate a certain item on the screen. Sort of Where's Waldo in video games. Items usually blend into the background - sometimes in clever ways - and the backgrounds are drawn in a way to make it hard to spot. In all the games I know the background is a static image, but I guess it doesn't have to be that way.

There are multiple ways to know which item you are supposed to spot - in some games you are actually presented with how the item looks like, other games only show you the silhouette and others just give you a textual description or a name.

Finally, many hidden object games also incorporate other genres - for example some are semi-quests in which objects you find are then added to the inventory as quest items.

Hidden object games are usually considered casual games and are priced accordingly. The giant casual gaming publisher Big Fish Games lists dozen of these games, with some of them sporting really gorgeously-drawn backgrounds (spoiler alert).