The infodumps in this episode are mildly annoying on rewatch, but tolerably so. Given that this is the episode that introduces Rakka to her new world a certain level of briefing is required.
This is also the first episode to feature the beautiful instrumental opening Free Bird.
The episode opens with Rakka attempting to get dressed in the morning whilst managing her new wings and halo. This is a somewhat painful exercise. Rakka then joins Reki and a number of the Young Feathers on the balcony.
Despite her memory loss Rakka can sense that this town is new to her.
One of the Young Feathers demonstrates clapping her wings together, Rakka tries it but only feels pain as a result. The other kids are basically full of mischief when the other Haibane return with breakfast.
The conversation over breakfast flows naturally and repeats the tradition that the Old Feathers are named after their cocoon dream. In contrast the Young Feathers name themselves after what they want to be, e.g. Hana (flower) wants to be a florist. 
The kids spill the beans about Reki’s name: pebbles, for the small pebbles on a long path that she was walking along on a moonlit path. Reki is very downbeat when she shares this and the speed with which the Old Feathers change the subject is telling.
The new subject is a trip to town through some beautiful scenery, but it reinforces how rundown Old Home is. This introduces Rakka to the fact that the Haibane are relatively rare, and that they only use used goods.  The dress that Rakka is wearing at this point is, charitably, embarrassingly ugly.
Kuu notices Rakka’s embarrassment and kindly suggests a shopping trip to a used clothing store. The proprietor of which looks like a grumpy sort, but is actually quite kind to Rakka. The Haibane pay using pages in notebooks, in lieu of this Rakka signs for the purchase and leaves a feather.
In other words there is another discussion about how the system underlying the Haibane works.
As the Haibane leave (so as not to get in trouble) Rakka is distracted by a crow  just like the one in her dream. Frozen for a moment she does not move until the Haibane Renmei Communicator startles the crow into flying away. This is the most significant moment in this episode, but it won’t be explained for some time.
When they return to Old Home, Rakka now has a name tag and a summons to the Haibane Renmei Temple.
Reki is sitting waiting for Rakka , which is just as well when Rakka collapses from overexertion. On the upside, Rakka no longer needs the holder for her halo.
Where the first episode is primarily about introducing Rakka to the viewer, this episode is primarily about introducing Rakka to the world. As far as I remember the infodumps go down smoothly for a first viewing as this is also new to the viewer, but do grate somewhat on rewatches.
As a result there really isn’t a lot of plot in this episode. The key points are the extent to which Reki’s name is a sensitive topic, and Rakka again facing the crow from her dream (but not realising that yet).
An essential foundation episode, and it is reasonably enjoyable. However much of the enjoyment is dependent on this being a first viewing.
Day 1 – Cocoon – Dream of Falling from the Sky – Old Home
Day 2 – Town and Wall – Toga – Haibane Renmei
Day 3 – The World of Haibane Renmei
Day 4 – Temple – Communicator – Pancakes
Day 5 – Trash Day – Clock Tower – Birds Flying Over the Walls
Day 6 – Dub vs Sub?
Day 7 – Library – Abandoned Factory – The Beginning of the World
Day 8 – End of Summer – Rain – Loss
Day 9 – The Gender of Haibane Renmei
Day 10 – Scar – Illness – Arrival of Winter
Day 11 – The Bird
Day 12 – ???
Day 13 – Well – Rebirth – Riddle
Day 14 – Kuramori – Haibane of Abandoned Factory – Rakka’s Job
Day 15 – ???
Day 16 – Parting – Darkness in the Heart – Irreplaceable Thing
Day 17 – Bell Nuts – Passing of the Year Festival – Reconciliation
Day 18 – ????
Day 19 – Reki’s World – Prayer – Reconciliation
Day 20 – Looking Back At Haibane Renmei
- Twenty Days of Haibane Renmei – Day 1: Cocoon – Dream of Falling from the Sky – Old Home (piratesobg.wordpress.com)