We make chords from clustering in thirds above each note in a scale.
All of the chords above have been written in Root Position. This means that the bottom note is the letter name or root note of the chord. Each note in the chord is a third apart. You can see this by the notes being on consecutive lines or in consecutive spaces.
A root position chord can also be referred to as a 
chord.
This is because the top note is a 5th above the root note & the middle note is a 3rd above the root note.
But we can play & write the same chords with the same notes, in a different stacking order.
We call this an inversion.
See below:
In the first inversion, the root note or letter name of the chord is now moved to the top. The top note is now a 6th above the bottom note. The middle note is a third above the bottom note. It is easily recognised by seeing that the bottom 2 notes are close together.
A 1st inversion chord is also referred to as a 
chord.
When using roman numerals it is often shortened to look like this:
In the second inversion, the root note or letter name of the chord is now moved to the middle. The top note is still a 6th above the bottom note, but the middle note is now a 4th above the bottom note. It is easily recognised by seeing that the top 2 notes are close together.
A 2nd inversion chord is also referred to as a 
chord.
When using roman numerals it looks like this: 
Slash Chords
In chord charts it is common to see a chord written like this: C/G.
This is referred to as a slash chord.The first letter represents the chord to play and the second letter represents the bass note to play.
A slash chord like this one is an example of an inversion. This is because the bass note is a note contained in the chord.
So in this example you would play a C chord with a G bass.
C/G is a 2nd inversion.