My forte` isn't explanations. Someone else could (and hopefully will) explain it in less words and clearer.
Just because the screen isn't infinite (let's say it's 800 x 600), the screen space is a Cartesian grid with x, y, axes that can go negative or positive.
Even if your screen is from (0,0) to (800, 600), the position (-100, -700) is outside of the screen's rectangle, but still in 'screen space' coordinates, because it's still relative to the same origin as the screen.
Everything in space is relative to some other position. There's no such thing as a 'position' except as a measurement relative to another point (the origin of your measurement).
A 'position' of an object is the distance between the object and the origin of the 'space' it is being measured in.
Where is the Earth located? You can give me the distance of the Earth from the Sun. That would make the Sun the origin, and you measuring the Earth's position in what we'll arbitrarily decide to call 'Sun-space'. Or you can give me the location of the Earth relative to the center of our Galaxy, making the center of the galaxy the origin.
Or you can give me the distance relative to the center of the universe, making the center of the universe the origin.
None of these are incorrect answers - they all refer to the same location (the location of the earth) but are in different coordinate spaces.
To convert between these spaces:
earthPosInGalaxySpace = earthPosInSolarSystemSpace + originOfSolarSystemInGalaxySpace
earthPosInUniverseSpace = earthPosInGalaxySpace + originOfGalaxyInUniverseSpace
Any 'space' is something that we make up. They only exist, because we can't measure anything (not position, not size) without measuring it relative to something else.
With 2D sprites, we measure 'size' at the pixel scale. We measure 'position' in a variety of ways, and we frequently convert between them as the need requires:
origin of the entire game world
origin of the area within the game world ("Green Forest")
origin of the subportion of the area that happens to be loaded around us
origin of the camera
These are just several possible coordinate spaces. At the very least, in almost every 2D game, you have 'world space' (what you keep your entity locations in) and 'camera space' (what is visible onscreen). Different people have different names for these - the names don't matter, the concept does.
If you say something is at position (0,0), you probably mean either relative to the game world, or relative to the camera - but it's important to understand which you want. Likely, all your API draw functions take screen-space coordinates. Likely, you'll want to keep all the objects in world-space coordinates. So knowing how to convert between spaces is important.
Thankfully, the formula is very simple:
originInNewSpace = (positionInCurrentSpace + originOfCurrentSpace)
In Johnell's case:
posInWorldSpace = (positionInCameraSpace + originOfCameraSpace)
posInCameraSpace = (positionInWorldSpace - originOfCameraSpace)