I am wearing my DM hat for this one and will be basing my answer as much as I can on personal experience or rules, so fair warning.
In the general sense, you encourage players to engage in certain habits by rewarding them for those habits. If you're the kind of DM who grants experience for good roleplaying, for example, getting the characters to go exploring is as easy as granting the party ranger a couple of points for each new area they visit.
Some parties, however, don't bother trying new things, and thus won't know that trying new things lead to rewards. That's where Passive Perception comes in.
Say your party is trooping through an area that you want them to explore in greater detail. Select the person with the highest Passive Perception and tell them they spot something odd- say, a jungle vine that has small, spotted leaves. Now, whether or not this actually means something (and this would be a great time for the druid or ranger to show off those skills and inform the others whether it does or not), you've got the party stopping to look. If, say, those leaves happen to grant advantage to a Medicine check when used in sufficient quantities, and if there just so happens to be about half the leaves the party would need on that one vine, you've just given them cause to stop for a couple of minutes and poke around, looking for another one.
This is where you can both encourage the plant-based members of the party to shine and give the rest of the party a chance to do something awful and interesting. The ranger and druid can obviously pick out those leaves again, as could someone with proficiency in herbalism, but to anyone else, it's quite reasonable to assume a leaf is a leaf. If you need someone to stumble upon poisonous things, or run into an angry giant ape, now's the time. Ditto for accidentally uncovering the entrance to a vine-covered shrine, or spotting a golden statuette half-buried at the base of a tree.
The key with this particular technique is balance. You don't want the party to run into something dangerous every time you call their attention to a detail- I once caused the party to run screaming from a windmill because I described a suspicious creak, having accidentally trained them that such odd noises led to surprise attacks- but you also don't want to liberally hand out rewards, because that leads to them pausing the game to search frantically every time you mention a detail.
Try to keep the details lumped into three roughly equal groups:
- Details that lead to rewards
- Details that are benign
Details that lead to "bad things"
You should end up with a party always questioning whether it's worth it to explore. If that cautious exploration is what you're looking for, then this is a way to achieve it.