Yeah, I mean, I've seen Plex be very popular over the years, but I've never understood why.
Unless you want on the fly transcoding (which I don't) why would you install an extra layer of software when network file systems like SMB/CIFS and NFS exist and are built in to their respective operating systems by default?
I think all the other responses missed the key driver. Go back 10 years ago and look at the TV landscape for HTPC. In one corner, we had Microsoft's MCE that handled cable card/DVR stuff but did zero streaming tricks. Sure, you could put a front end on it (RIP, Meedio) but then you lose the cablecard channels as you need an MCE Extender device. Netflix and other streaming services were starting to become mainstream as well.
Then, note that you have a family - a wife that things to "just work" and have the same user interface across the house (without having to switch inputs between the MCE Extender and Roku). Add some kids to that who want to watch Frozen in its entirety at least thrice per day on some screen (TV OR iPad). Let's not forget that any backup copy of the movies/TV that you have on your home server are all ripped in different video/audio encoding methods that may work on one device natively but not on another.
How did Plex solve that problem? Well, it was available as an app on Roku's platform, Android, iFruits and even worked on PC. It didn't care (much like the honey badger) exactly what codecs were used on the media as it would automagically figure out what to transcode it to on the fly to fit the device being served. Out of the house on limited bandwidth? No problem, it'll downsample things to fit that blazing fast 2.5G EDGE connection. It provided an identical user interface (that worked with remotes!) whether you were on Roku, iFruit, Android or whatever. It hoovered up the relevant box art and metadata based on the file name. It made things easy. Nothing else compared to it for quite a long time (and arguably, it still doesn't have much competition).
In short, it has generally made the media techhead of the family's life easy with its feature set, and that has driven its popularity (at least, in my opinion). We've been an all Roku household for a near decade across all of our TVs and I have zero ongoing issues that crop up. Those MCE Extenders were so bad, they still taunt me from the office shelf from under a layer of dust from time to time....
Ninja edit: While I'm at it, I offer a middle finger for Ceton for promising to fix MCE Extenders but never did.