When people discuss illegal search engines, what they typically mean are search engines that are designed or primarily used for accessing illegal materials. A search engine provides directions to a site, but it does not itself hold any of the site's materials, so it is usually not perpetrating a crime. In some cases, a search engine might be considered illegal in a specific country because that country does not want its population to have access to the information the site provides, even though that information is not necessarily criminal. Which search engines are illegal always depends on where someone is conducting the search, but in many cases, one that is illegal will be blocked in an area where people are not allowed to use it.
No matter the name different search engines use, there are really only two types of illegal search engines: those that provide access to illegal materials and those that are themselves illegal. Sometimes, a search engine might fall into both categories. There is no such thing as one that is universally illegal, and most can still be accessed even if they are blocked. Doing so, however, does itself often constitute a crime.
Some of these search engines are used as ways of accessing media for which a person might otherwise be expected to pay. For instance, copyrighted materials are often found on illegal search engines for free. The precise way in which these search engines operate varies, and the specific mechanism by which the materials are accessed have nothing to do with why these search engines are illegal. What is important, from the perspective of the law, is whether or not the person distributing the items has the right to do so, and whether or not the distribution violates copyright laws.
Search engines can also be considered illegal if they somehow threaten the government of a country, or the government dislikes them. Sometimes, a government may wish to censor materials and may not be able to reach an agreement with the company about which websites it will list. In these cases, the site may not even provide access to specifically illegal materials. The materials might show government officials in a bad light, or may offend certain powerful parties, but the words or images themselves might still be legal. Visiting illegal search engines is often a serious crime when the search engine itself, and not the materials to which it provides access, is deemed illegal.