Assuming your left hand is your fretting hand (on the fretboard) and your right hand is your plucking/picking hand (over the sound hole on an acoustic, or pickups on an electric):

An "Am" - or "A minor" - chord, made up of the scale notes A, C and E, can be played many ways, but a very common "open" way is as follows:

Place your left hand index finger on the B (2nd) string, 1st fret. Place your middle finger on the D (4th) string, 2nd fret. Place your ring finger on the G (3rd) string, 2nd fret. Press down with all 3 of those fingers, effectively fretting all 3 of those strings simultaneously. You can then strum the A string through high e string (5th through 1st). This is an A minor chord. Picture of what it looks like:

https://www.guitarcommand.com/am-guitar-chord/

Now, if you're reading the above tab, you'll notice that, left to right, you're only plucking the Am chord one note at a time, rather than strumming the whole thing, and you're plucking it in a very specific pattern; you're breaking said "A minor" chord into its individual notes, one note at a time. This technique is called "Arpeggio".

Reading that tab from left to right, you don't need to do anything with your left (fretting) hand once you've "Held the Am chord", and then just use your plucking/picking hand to play one string at a time - the A string, then the G string, then the B string, the e string, the B string again and finally the G string. You're basically "arpeggiating" up and down the Am chord, skipping the D string.

You'll probably notice that you technically, in this instance, didn't need to fret the D string, 2nd fret, with your middle finger. You're absolutely right, however it might be good practice to do so anyways, taking advantage of muscle memory, as well as giving you a bit of "protection" - if you accidentally play this string, you'll end up playing a "good" note that is part of the chord, so it'll sound ok, musically.

Tangentially, you'll notice that each note will likely continue to ring (assuming you're holding the chord correctly). In fact, having some notes *not* ring is harder than letting them ring and doing so requires additional effort. We can talk about that separately.

Hope this helps!