I wonder if you need any armor actually...
I'm gonna go with a portable riot shield, so read on.
Let's suppose the target is a human being, so mostly water. The energy to heat up one gram of victim's meat from 37°C to 100°C is 263 J, then 2.2kJ is required to vaporize 1 gram of water, so a 1kJ shot would at most vaporize 0.4 grams of meat, if delivered fast enough, via high power pulses.
Most likely it would remove less meat, as some of the high-power pulse would heat the meat to much higher temperatures (incl. into plasma) so this energy is not available for vaporization.
So, the target now has a tiny dent in their skin, with a cloud of superheated steam/plasma exploding around it at enormous pressure.
I guess the damage mechanism to a human would have a lot more to do with the resulting pressure and explosion than the burn. The 1kJ energy here is equivalent to about 0.2 grams of TNT. Not a lot, but you can already shoot a pretty deadly bullet with that. It's also the kinetic energy of a brick fast enough to turn a skull into a watermelon. Of course only a small part of this would damage the target, but it would definitely result in a bloody mess!
Now, we could use a more powerful laser to really make their head explode. Say 100 kJ instead. But then you have a problem: if you miss the bad guy and hit, say, the nice window overlooking into space instead, then the resulting explosion will be equivalent to 20 grams of TNT, and everyone dies. In fact, it would be a lot safer to use a shotgun loaded with buckshot, which tends to do a lot more damage to people compared to bulletproof glass. Also it would ricochet on bulletproof glass, whereas the laser will make it explode no matter the angle it hits...
Another fun thing with lasers is that if you hit, say, a nice sci-fi space craft wall made of shiny brushed aluminium with the 100kJ laser, then it will vaporize about 10 grams of it (handwaving 100% efficiency)... so now you have a nice cloud of superheated aluminium vapor...
At this point, it occurs to me (ant to everyone else on board) that aluminium nanoparticles are added into thermobaric bombs because they don't just burn in oxygen, they BUUUURN. The 10 grams of Al vapor yield about 300kJ through the fuel-air explosion.
So we have 100kJ lazzer blast plus 300kJ secondary explosion, which gives about 100 grams of TNT, so the spaceship goes boom and everyone is dead.
Okay, so if the purpose of the laser is safety, better use a low power one and don't aim at windows.
Now, the armor. Well, if it's made of kevlar (or space kevlar, diamond, UHMWPE, etc) then all this stuff is pretty much hydrocarbon-based, so the vapor will be very combustible too... So there will be a secondary boom. Same with metals (worse, in fact). If it's ceramics, well, watch out for the chemical composition, as pretty much everything will burn in oxygen if hot enough (boron, silicon...) and as for the answer above who suggested hydrogen of all things...
Water would be different, though: it would turn into a plasma of H and O atoms which would then recombine into water (ie, burn), but this would not bring extra energy to the blast, since the energy required to break down the molecules was borrowed from the laser, it is released again when the hydrogen burns.
So, here's my suggestion: you need a material which will probably be combustible once vaporized, while being able to soak up lots of water relative to its own weight, so that most of the laser energy creates non-combustible water vapor. This can be one of the super-absorbent polymers or hydrogels.
If you're in a real hurry, you can cut up a riot shield-sized piece out of a foam mattress, soak it up in the shower, and then use it as a laser-proof shield to charge at the enemy. You'll never forget the looks on their faces! If there's enough water in it, or you duct-tape it to one of these solid stainless steel kitchen pot covers, it will also (probably) stop frangible bullets.
Also, it is a riot shield, not in direct contact with your body, so the laser-caused vapor explosion will kick it back, but it won't shock your internal organs. All you need is earplugs, and as always when using lasers, safety glasses!
If you're in less of a hurry, you should optimize the water content, because this thing is gonna be quite leaky. If you want a readily available source of hydrogel polymers, remember it is a commonly used hydroponic substrate, and raid the hydroponics bay:
(I mix some of the stuff in powder form with the soil in my flower pots, it increases water retention).
Remember it is also used in baby diapers and, obviously, and perhaps ideally for plot reasons, menstrual pads.
You can also use "personal lubricant" products, or the slimy mucus your space alien buddies produce in copious amounts (no offense, guys).
Or even gelatin from the kitchen.
Basically anything that turns water into a gel and attaches it to a shield, or allows a bit of foam to be soaked and not leak, will work.
I don't suggest plywood as a backing material, it would spall when the laser explodes a bit of water. But any metal would work fine. Plus, as I said, if the water-gel layer is thick enough, it will also stop frangible bullets.
If you can get a large pan of Jell-O from the kitchen, it's a readymade laser-proof shield. Also you can eat it after the battle.
This would be quite heavy though, so you'll need to repurpose any kind of wheeled vehicle like a kitchen cart, or maybe a wheelchair.
If their lasers take 30 seconds to reload, you can probably kill them all with Jell-O and shivs.
Also, obviously, you can counterattack by making the air combustible.
Getting hold of a propane tank on a spaceship should be quite difficult, but you can just lob a kitchen bag of flour or corn starch over the enemy ranks, then hit it with your laser (try to aim carefully!). It will explode and disperse into the air as a very combustible dust cloud.
Flour (or sugar, etc) contains 4x more energy by weight than TNT. However it won't be mixed optimally with air, most of it will end up in the floor, but still...
Now, thanks to youtube, when you want a video of someone doing something very stupid with explosives, the question isn't if you gonna find it, but how many you're gonna have to watch before finding one that looks good!