To be extremely unacademic, in my head I consider the blues scale to be the "cool" scale. Whenever I hear it used in a song, it just makes the song sound and feel "cool." It adds fun, with just a slight bit of edge (owing to that dissonant tritone). Be it the Contra Base theme or Black Dog by Zeppelin
For some basics, the blues scale is the pentatonic minor (5 notes from the 7 in a minor scale) with a few extra notes, the blues notes, added. (I don't know if that's the actual name, but I call it that since it's what makes the blues scale the blues scale; hearing them is what gives it that sound). They are 3 chromatic notes--the fourth, the augmented fourth/diminished fifth (aka tritone), and the fifth.
Obviously, this scale was originally used in, you guessed it, the blues. Chuck Berry is the father of rock 'n' roll, and some of his most famous riffs and licks became trademark staples of rock guitar. Listen to his legendary "Johnny B Goode" or the equally iconic "Tutti Frutti" by Little Richard. These songs are on the border where blues first became rock 'n' roll. Then listen to songs like Steppenwolf's "Born to Be Wild" and Sweet's Ballroom Blitz. You can hear the similar riffs used in these songs, the same Chuck Berry thing where the guitars play a power chord (fifth), then hammer on a sixth and augmented sixth. This sort of thing is still used way into the 90s you can hear it in Alice in Chains' Man in the Box (albeit it's more subtle there). One of the most common Chuck Berry licks used all the time in rock and metal is doing a unison bend on the root note and then hitting its fifth on the string above it. The most obvious example that comes to mind is the solo on KISS' "Rock 'N Roll All Nite"
Another trademark of rock music that comes from the blues is the 12 bar blues progression (i.e. 4 bars of I, then 4 bars of IV, 2 again of I, 2 bars of V, and then repeat.) E.g. Rock 'N Roll - Led Zeppelin
Historically speaking too, most of the great rock musicians of the 60s were inspired by the blues players of the 50s. Mick Jagger is the original rock frontman, and he modeled his style after the black American blues players. The Stones are, after all, a blues rock band. The Beatles too.
Of course, rock eventually diverged and began incorporating everything else--minor, harmonic minor, major, modes of major scale, exotic scales in metal, jazz, you name it. But it began in the blues, and at the very heart of a rock song is usually the blues scale somewhere in there, be it the main riff or at the very least some licks in the lead playing. Kirk Hammett and Dave Mustaine for e.g. use blues licks in their solos all the time. The solo for the Mechanix comes to mind, and I'm pretty sure nearly all the songs on Kill 'Em All are based around either pentatonic or blues riffs. It would be quite rare to find any modern rock or metal song without any influence from the blues. Historically and culturally too, it was the blues players that became and inspired the original generation of rock 'n' roll.