Wiktionary
n. (context computing English) A text box for the input of text to be searched for in a database, on the Internet, etc.
Wikipedia
A search box or search field is a graphical control element used in computer programs, such as file managers or web browsers, and on web sites. A search box is usually a single-line text box with the dedicated function of accepting user input to be searched for in a database. Search boxes on web pages are usually used to allow users to enter a query to be submitted to a Web search engine server-side script, where an index database is queried for entries that contain one or more of the user's keywordresearch.
Search boxes are commonly accompanied by a search button (sometime indicated only by a magnifying glass symbol) to submit the search. However, the search button may be omitted as the user may press the enter key to submit the search, or the search may be sent automatically to present the user with real-time results.
Usage examples of "search box".
They took a circuit and then another one, reaching the edge of their search box, then pulled around and began again, retracing their steps backward.