A Traveling Spirit is a rotating visitor who shows up in Sky: Children of the Light for a few days at a time, selling cosmetics from their original season — emotes, capes, hair, masks, and music sheets. Check Sky Shard's homepage for whether one is visiting right now and exactly when the current one departs.
Traveling Spirits arrive Thursday at 00:00 Sky time and depart the following Monday at 00:00 Sky time — a visit of roughly 96 hours (it shifts to 95 or 97 hours on the specific weekends a daylight saving transition happens). They can be found in Home near the koi pond, or out in Aviary Village. thatgamecompany doesn't publish a forward calendar of who's coming; they typically post a puzzle teaser early in the arrival week, then a full reveal about 36 hours before the visitor shows up — so you usually know who's coming by Tuesday, not much further ahead than that.
Traveling Spirit items are priced in Ascended Candles, the same currency red shard eruptions and the weekly Eye of Eden run pay out. Ascended Candles aren't exclusive to Traveling Spirits, either — they're also spent unlocking a permanent Wing Buff from any regular Spirit's friendship tree, so budgeting matters: if you're saving for a specific Traveling Spirit item, decide in advance whether that takes priority over ascending a Spirit you already have unlocked.
Individual Traveling Spirits don't come back on any short, predictable schedule — a repeat visit from the same spirit is typically many months to a couple of years out, not weeks. Separately, thatgamecompany occasionally runs a themed "Returning Spirits" event, where a group of past seasonal spirits reappears together for a week or two — that's a different system from the weekly single Traveling Spirit rotation, and it's the more realistic way to eventually pick up something you missed, rather than waiting for one specific spirit's individual return.
Because the reveal only comes about a day and a half before arrival, the practical strategy is to keep a running Ascended Candle buffer rather than trying to save up reactively once you know who's visiting. Running the weekly Eye of Eden statues and catching red shard eruptions (see how to catch a shard eruption) are the two steady sources — between them, most active players can keep enough saved to act quickly once a Traveling Spirit is confirmed.