For the intro, a simple melody is played on the acoustic guitar. This instantly sets the mood for the rest of the song. Any specific emotions that the song communicates are difficult to define, as is the overall mood of the song, and I think it is this ambiguity that made the song so popular, as it makes it open to individual interpretation. I personally got a sense of melancholy dreaminess, however, the emotional atmosphere of the song is very much open to personal interpretation, giving the song a wide audience. It is the mixture of minor and major chords that McCartney uses that creates this unique emotional context to the lyrics.
Another thing I think contributed to the songs popularity was its simplicity. There are only three different timbres in the piece: the acoustic guitar, McCartney's vocals, and a violin. There is a memorable and relaxing rhythm to the piece, which is not created by a drum pattern, perhaps to keep a sense of calmness in the song. The song is also lyrically simple, with relatively few lyrics for a song, that are repeated. In the end, I think this lack of complexity makes this song very accessible to a wide audience.
The rhythm is also consistent throughout the song, making it a unique rhythm that can easily be identified as belonging to that song. All this gives it an iconic like quality, a quality that is common in popular songs. These elements, combined with the unique and interesting emotions it communicates, it what made this song stand out so much and become so widely acclaimed.
