"Martha My Dear" is a tribute to McCartney's Old English Sheepdog, not about a romantic interest as some would believe. When I listen, I like to think of Elizabeth Taylor's Martha from Who's Afraid of Virginia Woolf? McCartney's dog sentiments are reflected in the lines "silly girl," "you'll always be my inspiration," "see what you've done."
I forget about certain Beatles songs. This is one I re-discovered recently on The White Album. Its very McCartney: the chord progressions are clean and strong with a piano intro (played by McCartney himself), brass band, and a dash of slightly dissonant strings. As with many Beatles songs, once the song climaxes, it's quickly over.
McCartney said of the song in an 1968 interview "You see, I just start singing some words with a tune ... I don't ever write a song thinking, "Now I'll write a song about...' I do sometimes, but mainly I don't. Mainly I'm just doing a tune and then some words come into my head ... and these happened to be "Martha My Dear, though I spend my days in conversation.' It doesn't mean anything ... but those just happened to come to my head. So that's what this song is about... it is about my dog."
I love the lyric "when you find yourself in the thick of it / Help yourself to a bit of what is all around you"
Here's more information about the song from The Beatles Bible.