Yandex.Search is a small search bar located in the notifications bar that lets you run quick searches by keyword. By default, the app is set up to work with Yandex Browser, but it's totally compatible with other Android browsers as well.
Although by default Yandex.Search lets you search information on the Internet, it also searches your device as well. This way, if you want to look for a contact's phone number or any other piece of information, you can type in his or her name and quickly gain access to that person's profile.
Yandex.Search is a search bar that some users might find useful, but it's definitely not essential – especially if you already have a search bar installed, be it Google or any other of Android's usual providers.