Recommended characters, in the simplest form, are fan characters "recommended" by fans of BFDI(A). All of the recommended characters in BFDI last made an appearance in the last episode of BFDI.
In BFDIA, a "Top 25" mechanic was used, meaning that the creators used Google Moderator to choose the Top 25 recommended characters from all of the recommended characters according to it.
If you would like to recommend a character in BFDI, you can recommend it here! This link no longer works, as Google Moderator has been retired. However, you can now recommend characters on BFDI's sub-reddit, which can be found here.
Boombox is a recommended character that lives in Yoyleland which advertised the Leafy Detector, used to find Leafy. It was recommended by Anko6, who is the creator of another object show called Brawl of the Objects, in which another character named Boombox was in.
Gun is a recommended character that was supposed to appear in Return of the Hang Glider, but did not appear, due to guns possibly meaning a violence symbol. The only image of it exists in Carykh's BFDI Recommended Characters video.