This is a recurring motif and not just in every part of the Three Colors Trilogy, but also in La double vie de Véronique (starring Three Colors: Red's Irène Jacob).
Emma Wilson writes:
The linking device is rendered all the more evident in a repeated motif found in all four films. In La double vie de Véronique, Weronika, dressed only in her underwear, watches an old woman with heavy shopping from her window. Improbably she cries out that she is going to help her. We do not see whether this happens here: the scene appears to relate again, and instead, to the trilogy where, when each of the three protagonists encounters a figure bent over with bags, intent on putting a bottle in a bottle bank, it is only Valentine, in Rouge, who will help her.
(Emma Wilson, Memory and Survival the French Cinema of Krzysztof Kieślowski, New York 2017)
Film critic Dave Kehr wrote in 1994:
Other of the repeated elements carry a tremendous moral weight, acquired over time: a tiny, bent old woman, first glimpsed by Weronika hobbling down a street in Poland and later by Veronique in Paris, reappears in "Blue," struggling to deposit a glass bottle in the too-high opening of a recycling bin. Wrapped up in her own grief, June doesn't notice her, but when she reappears to Karol (as a man this time? the image is ambiguous), he watches her and smiles a rather cruel smile, as if her problems were only a comic distraction from his. Only when the old woman turns up in Geneva is there an act of recognition and intervention. Valentine, as she leaves the theater near the end of "Red," sees the old woman struggling and stops to help her, reaching up to drop the bottle in its slot. In a sense, that single, simple act of kindness is the climax of the entire trilogy, the gesture that saves the world.
And speaking about Three Colors: Red, Professor Kickasola notes (emphasis mine):
As he leaves, Valentine sees an old woman struggling to put a bottle in the recycling bin. Unlike Julie and Karol, who failed charity in their encounters with this situation, Valentine moves to help her. It is not only the redemption of this motif of the trilogy but also the fourth dilemma posited in the Judge's house, the helping of the elderly woman who wished to see her daughter. The glass shatters as it hits the bottom of the bin. Kieślowski, when asked about the motif, replied: "All I want to do is remind us that someday we might be too old to get a bottle into a recycling bin."
(Joseph G. Kickasola, The Films of Krzysztof Kieślowski: The Liminal Image, New York 2006, p. 318 (The quote is taken from "Insdorf, Double Lives, 181")
In an interview after his 1994 masterclass, Kieślowski talks about a screen personality and identifies important aspects, like "We want to get to know him, to see him react, to hear him speak." and that actor and character should share a similar attitude "Towards children, parents, his country, to the place where he's living. Towards the people surrounding him. His sympathies and antipathies, everything is very important to me."
So, in all four movies, Kieślowski exposes the main characters to the basically exact same situation - they have the possibility to help someone who needs it. It's important, since "someday we might be too old to get a bottle into a recycling bin" as quoted by Kickasola above. And by their reaction, we learn something about the main characters. It's like an experiment.
In a 1996 interview, Kieślowski summarized the meaning of the trilogy films:
For the sake of completeness, I will also add what he said about La double vie de Véronique in another interview.
La double vie de Véronique:
Live carefuly, because there are people around you, whose lives and well-being depend on your actions. This concerns all of us, because the paths - these people and their destinies - cross each other all the time, whether we are aware of it or not. That's what responsibility means to me - to live carefully and attentively. We should observe people around us, and most of all ourselves.
Three Colors: Blue
Everything connected with emotions and with objects or with any kind of commitment is a trap. It forces us to give up our freedom. Love also takes away our freedom.
Three Colors: White
I don't think people want to be equal. Everyone wants to be a little better. And that's true for good things as well as bad ones.
Three Colors: Red
"Fraternity" means sympathy, a willingness to help others. The hero tries to convince her that it doesn't exist, but her very presence proves fraternity is possible.
Now, let's look again how the main characters react to the same situation:
(regarding Julie in Blue, note that she is grieving and she is only free from it, when listening to music. That's what she does in that scene and why she doesn't react or even notice the old woman, although Kieślowski really makes sure we do.)
- Three Colors: Blue: Julie doesn't even seem to notice her.
- Three Colors: White: Karol notices them, but remains passive.
- La double vie de Véronique: Weronika/Véronique are at least willing to help.
- Three Colors: Red: Valentine actually helps her.
We see a progression (please note that this is not entirely chronological as La double vie de Véronique is older than the trilogy) and the final movie finally leads to the poor old person receiving help. It was the last film of the trilogy, the ending tying all the films together and also Kieślowski's last movie. At last, someone is not preoccupied with herself or disinterested, but wants to and actually does help. It's, as Kehr notes, "the gesture that saves the world."