Staying alive is important, but death in Sekiro is more nuanced than in Souls games. If you're killed in battle, the Wolf can use his strange power to resurrect himself. In fact, you can use death as a tool-- enemies will often wander away from you after you fall, allowing you to resurrect and sneak up behind them to deal huge blows.
The caveat is, you only get two chances to revive yourself, and after that, the consequences are dire. Like Demon's Souls, Dark Souls, and Bloodborne, you lose a huge amount of progress if you die and can't be resurrected. As you fight and kill enemies, you gain points you can use in progression trees to buy new skills and abilities for the Wolf to make him stronger; if you die, you lose half of all the points you've accumulated (but not the skills you've already acquired). The same goes for money, which is what you use to upgrade the Shinobi Prosthetic. Unplanned deaths seriously hamper your progression, and unlike the Souls games, you can't return to your own corpse to reclaim what you've lost.
What's more, death has further-reaching consequences than just slowing your ability to make yourself stronger. The more you die, the more a sickness called Dragon Rot grows in the world around you, and it can begin to afflict the people you've interacted with in the game. When a character you've met in Sekiro gets sick with the Dragon Rot, it'll change the ways they interact with you, possibly even stopping them from talking to you (or helping you, or selling you things, as the case may be). The sickness is represented by an item called Essence of Rot in your inventory, and you'll get one for each infected character. We didn't see what those characters' ultimate fates might be--Activision developers on-hand wouldn't reveal whether they could die in the name of holding back spoilers, but did say you'll be able to search for a cure to the disease to potentially the sick.
Though dying can be a huge setback in Sekiro, there is a chance you won't suffer the full pain of losing half of what you've earned every time. Sometimes when you die, a mechanic called Unseen Aid will kick in. This is basically a chance for divine intervention from the gods and Buddha, allowing you to keep all your experience points despite going to your grave. Unseen Aid has a relatively low chance of kicking in, though, and the more Essence of Rot you're carrying around, the lower the chance of receiving Unseen Aid becomes. The more you die, the tougher on you Sekiro can be.
So even with the revive system, death is a big consequence in Sekiro. Making sure you can avoid death's penalties has a big impact on how you'll play. You get two revive charges, but once you use them, each has a different requirement to restore them. One you get back from resting at one of the many idol statues in Sekiro, which are equivalent to the Souls games' bonfires, complete with the mechanic of restoring enemies you've already defeated to surrounding areas. The second charge comes from actually killing enemies--which means that you'll need to be aggressive when you return to the fight, or retreat to an idol (and respawn any defeated enemies) to protect yourself. Even if you just have the idol charge, you'll need to kill an enemy in order to be able to use it, though; you can't reclaim your own life without swapping one in return.