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.