Very broadly speaking, it means the song was mixed by the band. IE, once all the tracks are recorded, the levels of the instruments are mixed together, and the final sound of each instrument/voice is established (for example, adding reverb to a vocal or guitar). "Engineered by" (again broadly speaking) means the technical aspects of recording the musicians (setting up microphones, etc.) which greatly influences what the producer has to work with (the raw material of the recorded song).
For an example of how production can radically change the overall sound and feel of a song, see the rough or heavy version of "Why Don't You Find Out for Yourself" and compare it to the album version. Same song, same instruments, but a very different approach to production -- the former a heavy, live sound, the latter more acoustic and atmospheric. Or, listen to "The Boy with the Thorn in His Side" on the Queen is Dead vs. Rank. In the latter, the lead guitar, which is "low" in the album mix, is "upfront" in the live version. Same guitar sound, same guitar line, but wildly different feel based on the "production" or "mix."
There are deeper layers to it, but that's the 30,000 foot explanation.
The easiest way to think of it is that the Engineer is the guy who handles the hands on technical aspect of recording the session. The Producer is more of an overarching 'creative director', who will advise the band in which direction to take - ie "this middle section will sound better if we take out the drums, or add a guitar line here, that take was awful - do it again, or the tempo is too fast, let's try it this way etc".
The engineer records what people tell him to - it's the Producer's job to come out of the session with the best recording he can get, and direct the band accordingly.
What slightly complicates things is that there is usually quite a bit of blurring of roles in practice, so you'll get Producers who are also Engineers, or technically-minded enough to get involved in the mix, and the Engineer will often add suggestions regarding, and the band will frequently weigh in with both aspects as well.
"Originally, the song opened with a startling guitar prologue, hazily reminiscent of Buddy Holly’s ‘That’ll Be The Day’ intro, edited out in favour of a reverse echo fade-in. As on ‘Oscillate Wildly’, cut at the same session, Rourke was encouraged to add a cello part (though its middle eight, which originally featured a much more prominent cello line, was barely audible on the finished record). Marr would later enthuse to Melody Maker that the track possessed ‘one of the best rhythm patterns and grooves I have ever heard.’ In the same breath he also made a point of praising their rhythm section’s contribution with the amusing boast that ‘if Elvis Presley had had Mike Joyce and Andy Rourke in his band he would have been an even bigger name, I’m sure of it.’
Stephen Street wasn’t nearly so convinced. ‘I remember it coming out and I remember cringing thinking, “God, I really could have mixed this one better”. It just didn’t sound right and I wasn’t surprised when radio didn’t take to it.’ Journalist Nick Kent, who later attended the song’s mixing at Utopia studios, was one of many who blamed its production, describing the finished record as ‘an abomination of the song’s potential’. According to Kent, ‘it was a sobering example of the hopeless impracticalities of “group democracy”. Each member had his finger on the level adjustment dial pertaining to his particular instrument.’"
The implication being (implied above - all of) the band had more control over the released product's sound and that Street was not involved in mixing anything.
The sister alluded to in the title was Nimsy Shakespeare who was the sister of the famous Worcestershire cricket player William Harold Nelson Shakespeare. Some have speculated that Nimsy committed suicide, while others insist that Nimsy thought she could fly.