Autocomplete is to look for the matches of a given query and show them as a list of suggestions for the query. As the name suggests, an autocompleting algorithm tries to automatically complete a given query.
This has a couple of benefits. Firstly, it reduces the amount of time spent in entering a given value - we type in a query, a list of suggestions is consequently shown, we select one suggestion from it, and we are done. Secondly, it improves the UX of a webpage by making it look professional and performant.
Big names out there - such as Google, Facebook, Microsoft, Amazon - employ the use of autocompletion algorithms in their search bases to make their applications robust and allow for quicker option selection. Apart from these big names, autocompletion is now a general feature of the web.
Many libraries have been developed to power it on webpages, and many new dimensions have been given to it to make it even more powerful.