Through a variety of mechanisms
Blasters pierce, burn, and cauterize. They also have a decent amount of kinetic force.
A bright light. The bark of a blaster.
He cries out in pain as a laser
bolt burns a hole through his shoulder. His hand reflexively opens—the
microphone clatters away. He paws at his hip for his own blaster, but
another shot and the weapon that hung there is quickly spun to slag
and knocked off his belt.
Star Wars: Aftermath
Despite continuing the tradition of poetically (and inaccurately) referring to blasters as “laser bolts” even after that aspect had been dropped, this makes it clear that blasters can indeed burn through people.
Even more explicitly:
Cobb Vance’s hand is up in a flash—there’s the shriek from his own
blaster, and it punches a cauterized hole clean through Adwin’s
shoulder on his right side. His hand goes limp, lifeless. The helmet
clatters out of his other hand. He backs against the shelf,
Star Wars: Aftermath
Lest we imagine that this is merely the description of one novel:
“Tai-Lin.” She rolled him onto his back in order to assess the wound.
“Tai-Lin, can you hear me?”
But of course he couldn’t. He had been hit directly in the chest, at
close range, by a blaster set to kill. The deep wound where his heart
used to be had been cauterized, leaving a blackened crater behind.
Arliz Hadrassian had avenged her Amaxine warriors.
Star Wars: Bloodline
This also indicates that at closer range, blaster shots can cause rather explosive damage. Indeed, they seem to have enough kinetic force to blast a droid’s face off:
Norra’s on the ground—her back against the metal, her blaster up and
firing at a droid diving toward her. Her shot tears the thing’s
faceless mask off, exposing a sizzling circuit board. It collapses
against her, limbs flailing uselessly against the metal—she rolls it
off her and fires two more shots into its open skull. It stops moving.
Star Wars: Aftermath: Life Debt
As the new canon novels indicate, blasters are not clean weapons, nor anything like purely concussive. They are often not bloody, for much the same reasons as lightsabers (their intense heat), but nor will they leave only minor burns.
Stormtrooper armor can offer significant protection from blasters, as indicated in this question. Thus, the damage done to anyone wearing armor will likely be less significant than that done to an unarmored individual.
As to why the blaster wounds seem less gruesome against unarmored foes (in many cases) than these descriptions would suggest, there are several possibilies. Shots from far away are probably less lethal, in accordance with the increased lethality of nearby shots. Many wounds are cauterized, and so may not appear serious.
The moment the doors closed, Isval drew the blaster she kept in the
holster in the small of her back and fired into the back of Grolt’s
head. He collapsed without a sound. The shot from the small blaster
left his head intact, and the entry wound, cauterized by the blaster
bolt, didn’t even bleed.
Lords of the Sith
And yes, a packet of plasma fired at high speed may cause some serious concussive damage even if it does not burn through someone.