What does changing key mean?
Changing key means you need to sing slightly higher or lower. For example try this chord progression (La Bamba, or most of Twist and Shout, or many other songs.)
Key of C: Chords C F G
Key of G: Chords G C D
Key of D: Chords D G A
Key of A: Chords A D E
Key of E: Chords E A B
Any of these will work. The reason the song is still recognisable is because the relationship of the notes has not changed. (they are ALL raised/lowered by the same amount.) In all cases we have three major chords, starting with the I of the scale, then the IV (5 semitones/frets up from the I) and then the V (7 semitones/frets up from the I.)
These patterns are somewhat disguised by the different fingerings you have to do to keep the
chords near the nut, so try the following in order to see it more clearly (don't bother with the 1st and 5th string if you can't manage the bar chord. If you are using a pick or strumming with your thumb it's a good idea to rest a finger of your right hand on the 1st string to silence it.)
Key of G Chord G C D
Now add 2 to each of the numbers in the above tab and play again. Now you're playing in A (chords A D E.)
What is a key? (a simple explanation for strummers)
There are many ways to say what key is, but one of the most useful is to identify which chords belong to each key (that doesn't mean you can't play others, but it helps you to know which are most likely, and any that don't belong will stand out to your ear as being unusual.)
Another very useful thing is the cycle of fifths, which is covered elsewhere and you should learn all you can about. It's basically a series you get by going up 7 semitones/frets at a time. Here it is in brief.
Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A#
And here's the same thing in a zigzag (which is easier to remember because the notes on each line are consecutive, but is not as fundamental in concept.)
Gb Ab Bb C D E F# G# A#
Db Eb F G A B C# D#
You probably know that every major key has a relative minor key, for example C major / A minor. It's easy to pick out the chords that belong to this or any key from the cycle of fifths, according to the example below.
The root notes of the three major chords of C major fall consecutively in the circle of fifths: F C G with the C in the middle.
The root notes of the three minor chords of A minor fall in a similar pattern: Dm Am Em with the A in the middle.
As I said A minor is the relative minor of C major, and additionally you will note F C G is followed immediately by D A E the cycle of fifths. So you will find that many songs use exactly this group of 6 chords F C G Dm Am Em and those are the songs in the key of C.
I hope this is useful to you in knowing which chords belong to a key.
As I say, these are the basic rules, but musicians are free to break them (and nearly every exception to the rule is well studied and has a name.) The most common change (so common I can't even call it bending the rule) is the sustitution of a minor chord by its major version.