"Little Black Submarines" isn't about anything. The song, generally, is about lost love, heartache, etc. But the "little black submarines" line is probably a placeholder lyric that just stuck.

When songwriters are searching for a melody to the chords they're playing, they just fill in whatever words feel right, even if they're total nonsense. After the melody is set, then they go back over and smooth out the placeholders so the song makes more sense as a story. Here though, the guys just thought "little black submarines" was funny or unique and kept it in there. I love this song, but the rest of the lyrics aren't particularly engaging. Keeping those lyrics in the song, even if they don't make sense, gives the song character.