There are different ways to add additional harmony notes under (or even above) some or all of the melody notes.
In the parlance to which I am accustomed, "block chords" refers to a specific style of doing that, which involves harmonizing every melody note (for a section of the tune at least--rarely for the whole thing) with two, three, or more extra notes underneath it. So basically, everywhere there used to be a single melody note, there's now an entire chord of some kind with the melody on top. The chords don't add any additional rhythm--they're played in lockstep with the original melody.
And there are several ways to do it too, involving choices on whether or not you just use one hand or both, whether you put all the notes in the chord right next to each other or shift some down an octave to leave more space in the chord, etc.
I believe it started with piano players like George Shearing and Dave Brubeck, who in turn were copying the way the horn section would often be arranged in a big band. Accordion players like Ernie Felice and Art VanDamme were no doubt inspired in turn by the piano players.