One might understandably assume that using this field would look for files within the current folder. Instead the default behavior is to search your entire Mac, a behavior with which I associate the Spotlight icon in the Menu Bar. However, there is a way to set it to search within the current folder and it's a pretty simple task to do so.
Finder's “Advanced” Preference Tab
To change the setting, head to Finder preferences by switching to Finder, clicking the Finder menu in the Menu Bar, and selecting Preferences (or using the ⌘, shortcut). In Finder Preferences, click the gear marked “Advanced” and under “When performing a search” select “Search the Current Folder” to change the default.
This setting will only change searches performed within Finder windows. If you ever want to search your whole Mac during one of these searches, just click “This Mac.” Enjoy!