My personal way of letting my players know "out-of-game" of how the world is going to react to their characters "in-game" is to use the metaphor that I know sends some folks around here running for the hills... think of the game as a movie.This is a great insight. It is hard. As DM you want players to value those intangibles.
One way I've found, though I struggle like many, is to lay out subtle clues that the world is becoming aware of them. Suppose they go to a nearby town and enter the tavern. Then someone just asks, "Are you all the ones that slew the Gnoll King on the weathered heights?" Provide a little awe from the community.
There is also the other side of the coin where the players think they are world beaters at seventh level and have little regard for the niceties of diplomacy. This usually also requires a world like response.
The key I think is good narration and having a verisimilitudinous world. For example, a guide bringing the group to see the King after a successful quest on the King's behalf, their guide might whisper, "Oh that is Sir Trawnley, his armor is worth more than the Duchy of Unstol". You want to make your NPCs really good and you can provide information narratively via the NPC.
Still it is a delicate balancing act. You want the PCs to feel their growing respect.
I've toyed with a reputation score that only I kept. I might also have a list of allies and enemies. Maybe each one has a note on the strength of their feeling and why.
In almost all cases... if we all just imagine the situation the roleplaying game characters are in as a movie scene rather than a "game"... what would be the prototypical action and reaction from all the participants and characters in this scene? What would we expect to actually usually happen? And what is it that the players actually WANT to have happen, and thus how should they temper what it is that their PCs are doing?
In some RPGs it's easier, because they are literal games based on movies and TV shows-- Star Wars, Star Trek, Ghostbusters, James Bond, etc. So telling a player "If this was an actual Star Wars movie or tv show or novel... what would be the most logical action and reaction in the Star Wars realm to what you are having your PC do?" is probably easier for a player to perhaps get into the proper mindset for that style of game the GM is running. But for some RPGs that aren't tied to film or tv properties (like D&D)... the idea of treating what is happening in the game with the same internal logical story consistency of a tv show or movie is not a lot of player's first response. But bringing them gently along and giving indications of what "would normally happen if this was a movie" makes it easier. It'll still take time for them to evolve their thinking in that direction for this particular game... but one can get there eventually.
The most obvious scenario (in D&D especially) is meeting town guards. PCs do something or come upon something in the street... the town guard show up and inquire what is going on (with whatever personality traits the GM gives them). For a lot of players, their first reaction is "The guards are a roadblock to what we are trying to do! Kill the guards!" And it is at that point when I will step in with the gentle "If this was a movie... would the heroes of this story really attack these guards for just doing their jobs, no matter how gruff or pushy they might be? And how do you think the reactions of the rest of the town would be if the heroes did that? Do you think your characters would garner no reaction whatsoever and could just continue to go about their business?" And this is where they really start to grasp the whole "actions have consequences" thing, and by thinking of what they are doing in movie or story form... they can more easily put 2 and 2 together to figure out what the results of their choices will be.