By getting the players and their characters emotionally invested in the world … and then leveraging that investment. Both of my RPG entries for #RPGaDay2018 — “Most memorable NPC” and “Favorite recurring NPC” — used this technique.
Damocles Everton worked because the players were already heavily invested in the Blackrazor Guild, having saved it from the brink of bankruptcy. Damocles coming in and seizing control of the guild — not to mention offing its former guildmaster and killing one of the PC’s mentors — set the stakes for the adventure. The entire “Fall of Obsidian Bay” story arc then continually raised them by extending the threat to the heroes’ home city.
The death of Calvin Cloudmore — a longtime NPC — drew the heroes into the murder mystery that culminated with the reveal that one of their own had been possessed by a shadow demon and had killed off Cal as well as several other people on the PC’s grudge list.
I’m not saying you should kill off a favorite NPC character every time you’re trying to make the stakes important … but it can be remarkable effective.
Threatening the player character’s accomplishments works well too. Throwing the heroes’ starship into the Star Wars threatened the ship and heroes aboard it. The skill challenge that followed is legendary in our group and led the vessel being covered in “starforged armor” (aka the melted exterior of the ship). In our prequel campaign Obsidian Frontier I threw a blizzard at the fledgling town of Obsidian Bay. There wasn’t any danger of the city itself being wiped out — after all, the PCs knew it would be around 80 years in the future — but it caused misery in the city, wiped out many of its ad hoc, poorly constructed buildings, and set up the possibility of protracted suffering among the town’s population. Those stakes led the PCs to mount a mission to seek humanitarian aid from a neighboring nation.
Regardless of the hook, the key to making the stakes matter is to get the players invested in the world enough that they care about what happens there.