Board Thread:Questions and Answers/@comment-2.122.199.184-20141111223147/@comment-1298029-20150505213200

Well, I always interpreted it so that (in the movies, didn't read the comics) the skull is the Totenkopf (which is just German for "skull") skull of the real-world Schutzstaffel (SS, Nazi party elite guard/military arm), which Hydra began as a division of. That Schmidt became an actual "Red Skull" seems to me a case of "became on the outside what he already was on the inside" (i.e., Devil personified/the Nazi evil personified, ironically of course that's what he got when he wanted to become the Nazi ideal of "ubermensch" (literally, superman or superhuman)). It's quite symbolic, the evil being seen through the lofty bullcrap rhetoric.

As for the tentacles, for one, an octopus is not PR's favourite animal (despite real octopi being quite fascinating creatures, actually), as more often than not it carries negative connotations (kraken, generic sea monster, ugly, squishy, gross, weird, unnatural, etc.). Also, tentacles are fairly often associated with the quality of being far-reaching in influence, usually with a sinister and clandestine overtone (e.g. a nefarious organization, corruption in business or politics, behind-the-scenes control, etc.). Both of these fit Hydra well. Finally, the many tentacles may symbolize (modern) Hydra's many "heads", a compartmental structure, always some backup somewhere, omnipresence (as in the Shield infiltration, they really were in almost every team or department), etc.

So, overall, the symbol for Hydra both recalls its origins and founding philosophy ("new world order", which always remained from the Nazi era, even if they did abandon the narrow definition of Nazism even before the end of WWII), symbolized by the skull (which also, by an in-universe coincidence, evokes its founder), as well as its modus operandi (see above), symbolized by the tentacles. It's true the symbol doesn't have that much to do with an actual hydra (although the multiple tentacles still work for symbolizing the "heads"), but I think it's a very effective, well thought-out symbol on the part of the writers.

The S.H.I.E.L.D. symbol lends itself to similar analysis (which I won't bore you with here, unless you ask).

Anyway, that's my take.