hey dovey when somebody talks about the inversion of the chord they are talking about how the chord is voiced! basically, it has to do with what note is acting as the bass of the chord. for example, ill use a c major chord. you have a c, an e, and a g. that is a basic c major chord in "root position (because the root of the chord is in the bass). we use the number 5/3 (usually they are written vertically with no line) to describe that. that is known as figured bass. now, there are two other voicing this chord can have. the first option is first inversion, which is called a 6/3 chord. in this chord the 3rd is in the bass, therefore spelling the chord e, g, c. its called 6/3 because of the intervals between the chord members from the bass. you start counting from the top. an e is a sixth from the bass, and a g is a 3rd from the bass. (with root position, g is a 5th from c, e is a third from c). then the 2nd type of inversion you can have is 2nd inversion, or a 6/4 chord. now yr g is in the bass and it is voiced g c e. e is a sixth from g, and c is a fourth from g.
7th chords can be inverted too! yr root position works exactly the same. in first inversion, e would once again be in the bass and it would be voiced e g b c. the figured bass for this chord is 6 5 3, which is usually just shortened to 6 5. now the interesting thing with 7th chords is that you have a 3rd inversion, which puts b in the bass, voicing yr chord b c e g. the figured bass for this is 6 4 2, which becomes 4 2.
now there are a few more things to note, which just apply to tonal music (bach and kids, up to the 19th century.) you will never find a 6 4 chord in bach, just cause they didn't do that stuff back then. the only place you will find it is in a cadence, and its always controlled by a dominant (V) harmony and the chord goes to root position before ending on I. Also, you will never find a diminished chord in anything but first inversion. That's just how it evolved. Of course, in the 19th century all these rules start to get bent as composers stated doing wackier and wackier stuff until you get till today, where you can basically use this knowledge any fuckin way you want.
(note: on the topic of inversions, those are all of the things i know. i can expand upon anything here though if yr still confused.)