Probably any hand where you are not sure where you are at. JJ is notoriously tricky because the "high pocket pair" has really good
equity, but it loses to pretty much all "premium hands" that would easily continue against you. Same goes for AK or AQ when they miss the flop. It is difficult to assess if your hand is still the best or if you are behind already. This is the same reason why playing Ace-rag (like A2 or A6) or Paint-rag hands (like K4 or Q5) can be tricky or not advised. Let us take the example of K4 offsuit. We continue with this hand and we just got lucky by hitting top pair! Say the flop is something like K, J, 3 rainbow board. Okay great: but now what? If we bet and the opponent plays back, then they may have us crushed and if we slowplay by checking a lot, then we may lose a lot of value if we were far ahead in the hand. Let us say that in this situation, we bet the flop and the opponent re-raises us. This is a tough spot to be in. What if they have top pair as well? Then they probably have a better kicker than our low number (4 here). Something like AK vs our K4 is really bad for us.
Complicated hands are probably the ones tough to figure out if we are ahead or behind. How can we make profitable decisions, consistently, when we don't even know where we are at in the hand?
Not every hand plays this way. If we have pocket Aces, then we can safely say we are ahead preflop (of course with 85% equity or so versus a random hand, the 15% "bad beats" are still expected even if we are ahead now). What if we have 72o? If we decided to play it and the board didn't help us out, then it is an easy fold - we know where we are at in the hand (and therefore cut our potential losses by continuing when we are dominated).
In my opinion, "complicated" hands are usually ones tough for us to assess how we compare to opponent(s), regardless if we hit or miss the community cards.