I’ve already answered a related question from a linguist’s perspective: Nick Nicholas’ answer to What makes Modern Greek an interesting language to learn, from a purely linguistic point of view?. But this question really should be about a lay description.
(But I can’t resist telling Ilir Mezini: it’s Albanian, missing half the letters, and with even more Greek words in it. 😉
Modern Greek is a historical battleground, caught between its ancient heritage, and its more recent, variegated past. Lots of texture and hidden battles in there, of which only some have been resolved, and many have been resolved only recently.
It’s a staccato, rapid fire, impassioned language—although you should listen to some regional accents; Cretan and Cypriot are pleasantly sing-song, in different ways.
And of course I will use the Cretan Muslim village of Al-Hamidiyah in Syria to illustrate. Contrast the intonation of the journo, straight outta Athens, with the locals’:
As Indo-European languages go, it has rather more grammar than you’re used to, including some entrenched randomness in the verb system (sigmatic vs asigmatic aorists), random genders, and an accusative and genitive.
Compared to Classical Greek, it is drastically simplified, and the simplifications mostly are rather sensible. Although a classicist I once asked did say it looked like a drunk Ancient Greek.
If you speak a Balkan language, as I alluded above, a lot of its syntax, idioms, and morphology will look rather familiar.