Matt Smith's first episode, "The Eleventh Hour", brings in a new, exciting iteration of the Doctor and also features several things that become important to the Matt Smith era of the show. Doctor Who constantly has several strands of storylines that are ongoing and always expanding upon each other; with each new Doctor, it's common for the show to have a fresh take on show-regular aliens and villains, as well as add completely new creatures and characters. "The Eleventh Hour" doesn't disappoint.
Matt Smith's debut episode sets the groundwork for his close relationship with one of his most treasured companions, explores his new fashion sense, and, of course, features a face-off with an alien--displaying just how the Eleventh Doctor intends to get things done.
The Duck Pond
The duck pond in Amy's town is something to remember because it comes back to play a significant role later in the show.
The pond is first mentioned when the Doctor and Amy are running through her town and she refers to a tiny, unremarkable body of water as a duck pond, something the Doctor finds ridiculous due to the fact that there are no ducks in it.
The Crack In The Wall
The crack in young Amelia Pond's wall seems at first as though it is unique to the episode that fans meet Amy in for the first time, but little did they know that the crack would become an important piece of Matt Smith's time as the doctor, merely originating in his meeting with Amy but moving far beyond this point.
Meeting Rory
Fans meet Rory in the same episode they meet Matt Smith's Doctor and Amy. It's appropriate that the trio should come together at the same time, seeing as they spend so much time traveling together throughout the show and eventually becoming, according to Smith's Doctor, at least, some of his closest companions of all.
Amelia Pond
Amelia Pond, not be be confused with Amy Pond, becomes an entity of her own. Fans don't spend much time with her before the Doctor zips off and messes up his time calculations, resulting in his next meeting with her being when she has become Amy Pond, but young Amelia is held dearly in the Doctor's heart and continues to be lovingly considered "the first face this face saw", as the Doctor puts it.
Leadworth
Leadworth is the town that Amy grew up in, and the very town that the entire episode takes place in. The Doctor spends a significant amount of time making fun of the town for how small it is and how few shops it has, among them merely a post office that, he complains, is shut--but the town, like many things in the episode, becomes key to many larger things at play later in the series.
Amy's House
The episode opens on Amy's dreamy, fairytale-esque home in the English countryside. As the Doctor says, the name Amelia Pond sounds very fairytale, only further emphasizing the children's book charm that emanates from the episode--to the point it's a bit eery, and, as viewers find out, for a reason.
The Doctor Finds His Outfit
Each Doctor takes on a new body, but with this body come other changes. A new actor, of course, an updated Tardis, usually a new companion, and always a new outfit.
It's exciting for fans to watch and anticipate what particular style a new Doctor will select, and in Smith's case, the Doctor finds his personal style by the end of the first episode, donning what will become his well-known bow-tie and suspenders.
Olivia Coleman Appearance
Although not particularly relevant to the plot or important for later episodes, it's still fun for fans to remember details from a show pertaining to particular quirks of an episode or big-star appearances. In this case, the star at hand is the Olivia Coleman, made more interesting now as her fame has since blown up.
Homage To Past Doctors
There's a nice moment nearing the end of the episode when the particular Alien's at hand are face to face with The Doctor and, not recognizing him, do a scan of his personal history. This allows the opportunity for the show to highlight who the Doctor has been in the past and therefore featuring a small homage to all of the actors who have embodied the doctor and a general nod to the deep history of the show in general.
The Doctor Re-Asserts Himself As Earth's Protector
The Doctor is well-known as the defender of planets in need--in particular, the planet Earth. Long-time fans are fully aware of this, but with each new iteration of the show it's not uncommon for new fans to jump on board, fans who might not begin the show from it's earlier days and therefore not be totally in tune to the key components. To remedy this, the show will often take a moment to re-assert some of its foundational aspects. It does just this in having the eleventh Doctor call back the aliens and make sure they know that if they want to mess with Earth, they'll have to go through him.