Star Trek: The Next Generation was a worthy, if somewhat lesser, heir to the Original Series. It stumbled a bit out of the blocks, as many new shows do. Wooden acting by performers still feeling out their characters. Derivative writers groping for the tone and heart of the original with copycat scripts. Eventually, the crew of the Enterprise-D managed to squirm out from the shadow of their predecessors and establish their own identity as fine science fiction in their own right. But it took time, and some of the early episodes are nearly unwatchable in retrospect. It's interesting - when trying to copy the original, the show was borderline awful. When doing something new and creative, it thrived.
One thing they got right in the first episode was the character of Q (even this inventiveness owes a debt to the original series - Q was clearly a compatriot of Trelane, the Squire of Gothos). Due in large part to John de Lancie's jovial and charismatic portrayal, the godlike antagonist Q was an immediate shot of adrenaline to the new series. In some ways, he was too much, too soon - the new characters on the bridge struggled to keep up with his scene-stealing performance, even the decorated Patrick Stewart seeming unsure of just how to play opposite such lusty panache. It gave the sense that this new crew was out of their depth, on both sides of the fourth wall, and while it might have slowed the initial establishment of some of those characters, in the long run it was beneficial. Q served as the yardstick against which the growing, evolving ensemble could measure themselves. Each time he visited, you could see how much more surefooted the actors (and, by extension, their characters) became.
Beyond his contributions to the overarching narrative of the show, Q was an utter joy to watch. Episodes in which he appeared were singular treats for the audience, the very best of a series that became better and better as time wore on. He was unpredictable, dangerous, serving as the perfect foil to Captain Picard's stuffy stolidity. His withering critique of humanity was painfully accurate, puncturing the smug self-satisfaction that suffused the Next Generation. Mankind was still a babe in the interstellar woods, despite the Federation's complacent confidence. (An aside: this might be the biggest difference between the first two entries in the Star Trek franchise. Where TOS had the sensation of pioneers on the wagon trail, holding things together with their bare hands as they rocketed to the stars, TNG always felt a little too safe, a little too comfortable.)
Q constantly tested the crew, using his apparently limitless powers to tempt and temper them. To prove his theorem that humanity was overmatched, he accelerated the encounter with the Borg, perhaps the most pivotal event in the entire run of the series. Was he just messing with them, a dilettante slumming with the little people, a scientist with hamsters, a little boy with ants and a magnifying glass? It's never quite clear.