Chords are 3 or more tones played together, yet when we play 2 tones together, this can pass as a chord. Another word for chords is harmony. Harmony is the vertical dimension of music. Below are the 'starting points' for R5 chord shapes, sometimes called power chords. These are neutral, which means that they are neither Major nor minor and can work for both.
These chords above can be called power chords. This term can have different meanings to different players at different times. For now, memorize these chords, & know that they can be called power chords. These chords are R5's, which means Root-5. The Root is the name of the chord (what it is built from), the 5 is the tone that is 5 tones away from the root [A5 = AE = 12345 = ABCDE].
We can add another root on any of these chords to make the chord R-5-R.
A chord progression is a stream of changing chords over time. We write the chord symbols (we are using E5, A5, & D5) above a line with the rhythm [rhythm notation]. Notation is written music (there are many types). TAB is one type of notation, this rhythm notation below is another.
Play this progression until you have the transition between the chords (plan ahead), while keeping it in time (playing the beats evenly).
By knowing these 12 chords, you can play 1000's of popular songs. Whether a song is using these particular type of chords, you can still 'substitute' these for the chord symbol you see. Example: you see a progression G-C-G-D, you could play G5-C5-G5-D5.
You know this one.
We can also add another root to the shape. This creates an octave between the 6 and 5 strings. These shapes are still R5 chords [no 3rd present].
As with everything, we write our own progressions. 4 chord progressions are the most common. Start there.
Power chords are typically a rock guitar type thing. However, the term can be used for piano and other chordophonic instruments, & by other styles than rock (such as jazz or pop or folk, etc.).
What are they exactly? This an interesting question. We'll define them with 3 ideas in mind (what we'll call the 3 criteria).
These are subjective lines we draw for ourselves.
Voicing: Typically these chords have only a root and 5th in the bass of the chord - creating an interval of a 5th (a Perfect 5th - P5). In this instance (and in the example above), the root is the lowest tone, & the 5th (the tone 5 up) is stacked on top of this root, on the next string. These chords are known as R5 chords (Root-5th). They are a fragment of a larger form. In this case, the E form.
It sometimes happens that players use the tones in the opposite stacking order too (5th as lowest note, then the root). In this instance, the interval is 4th (Perfect 4th - P4), yet this 'isn't as powerful' (see Relative Strength below).
The simplest definition of a power chord may just be: any chord with a root/5th in the bottom of the chord. For this definition, full versions or non-fragmented chords, such as your basic E, could be called a power chord (since what we call a power chord - R5 - is within the full version). The full version of an E or A form moving up the fretboard could also be called the same (they have the R5 in the lowest tones).
Relative Strength of Sound: A power chord should stand up to its name. It should be powerful. Yet, where does the line get drawn between power and not power? Typically, for the strength to get the name, it must be in the lower range of the frequency spectrum.
So the question here is, at what pitch level is a chord with a P5 (or P4) no longer a 'power chord'?
Also, to get the strength, does your distortion have to be cranking? Not necessarily. Acoustic guitarists (with or without distortion) utilize these types of chords.
Application (Style Usage): These chords are typically used in rock & punk music. Most Green Day, Scorpion, & Ramones songs use them. Jazz players use R5 chords sparingly.
If a jazz song happens to use a 'power chord', they wouldn't necessarily be called that (they might just be called a voicing). Similar to hammer-ons (hammers) and pull-offs (pulls) in classical guitar, simply being called slurs.
In summary, we use the term power chord, most commonly, to refer to chords with a root and 5th only, where there is a strong strength of sound, & used in rock & punk guitar music.
Every guitar style has particular voicings which define its overall sound.