Unity is a game engine. You can think of a game engine as all of the core systems in a machine. Let's picture a space ship. Say you want to build your own space ship. You can start by scratch and build the zero-gravity engines, the life support systems or even the door controls. That would take a lot of work and time. Now imagine if there were someone that gave you all of those "standard ship systems" already built so you don't have to worry about "re-inventing the wheel", and just focus on the things that make your ship different and interesting. A game engine is a group of pre-built virtual systems that are necessary for every kind of game to function.
The Unity Editor is the software front end of the Unity game engine. This Unity Editor is the program you use to make games in the Unity game engine. You might read only the word "Editor" many times in forums or in the official Unity documentation. Now you know that "Editor" refers to the software interface you use. You can think of the Editor as "a Photoshop for making games".
The Unity Editor, for the most part, uses a modular user interface. Many of the windows, or panels, you see as soon as you open the program will have a little tab with its name, at the top-left of it.
At the top of the Editor, right below the menu bar, you'll see some buttons. These buttons are not movable, which makes them unique, since almost every other part of the interface is customizable.
These are the "transformation tools". These tools allow you to modify the 3D properties of objects in a scene.
These buttons are for testing a game. You won't need to use them.
I will only explain the last two buttons, as the first three are completely irrelevant for us.
Below this top bar of buttons, you have the main real state of the Editor interface. This is the area where all the windows are docked. I'll explain the default windows.
This is the Hierarchy window. By default, it will be docked to the left side of the Editor.
This panel will list all of the GameObjects residing in the current scene. This default scene contains a camera, and a light. As you create more GameObjects, you'll see them here.
This is the Scene window, with tabs for the Game and Asset Store windows to the right. The Scene window is a viewport that shows the current scene. A scene in Unity is a 3D world that you populate with your characters, world and code. You can think of it as a level in a game.
The Inspector window shows information about the selected object.
You will see a list of Components, with all of their editable properties shown. A Component adds functionality to a GameObject. This GameObject called "Directional Light" has a Light component, which will give it the light functionality Unity comes with.
This GameObject also has a Transform component, which determines all its 3D properties.
The "Add Component" button is one of the ways to add more components to a GameObject.
The Project window, is like a tiny Windows Explorer. On the left has a tree view of all the folders and files of your Unity project, while on the right, a view that shows the contents of the folders.
Lastly, the Console window will show any errors Unity encounters. Mostly used for debugging.
You can open any window using the Window menu.
When working with the Unity Editor, you normally don't need to save changes to the project files. For example, creating files, renaming files, moving files. These tasks don't need saving. The sort of things that have to be saved are the changes you make to a scene. Changes to a scene are creating GameObjects, adding or modifying components, nesting GameObjects, etc. To save a scene, just go to the File menu and click on Save, or Save as. You will then be asked to choose a folder. It is important to mention that you should only save your scenes inside the Assets folder of your Unity project.