Nidavellir is the homeworld of the dwarves in Norse mythology, and in this game you're building an army of dwarves, with the value of that army being determined by its collective bravery value, along with the sum of the coins you use to bid.
The game lasts two ages, and in each age you have 3-4 turns, with each turn consisting of the players visiting three taverns to recruit dwarves for their army. Each player starts with five coins — 0,2,3,4,5 — and you secretly place bids on your own player board for those three taverns, with the remaining two coins being placed in your purse. Everyone reveals their first bid, with ties being broken based on numbered gems, then players each draft one dwarf based on the bidding order, swapping gems in the case of ties. Then you reveal the second and third bids and do the same thing again.
If you reveal your 0 bid, you choose late at that tavern, but you sum the two coins in your pouch, then take a coin equal to that value from the bank, then discard the highest coin in your pouch. This boosts your bidding power in future taverns, and you earn more points at game's end for your coin stash.
When you have the first rank of all five types of dwarves in your army, you collect one of the heroes on the side of the board. In the image above, you can see that I took one of the orange heroes that adds three ranks with only one card. This both boosts the orange scoring — which is computed by multiplying the number of your orange ranks by the sum of your orange values — and makes it so that I don't have to worry about getting more orange cards in order to complete more ranks.
You want to get sets of all five ranks in order to collect more heroes, but you also want to specialize in colors since the more you get in a color, the more valuable (in general) those later cards are. A purple rank is worth 3 points, then 4, then 5, and so on, so you want lots of purple, but green is worth the square of the number of green ranks you have, so you want lots of those, too.
After the first age, a bonus is possibly handed out for each color. If one player has more ranks in a color than each other player, then that player receives the bonus in that color, which might allow them to upgrade a coin or gain a bonus card or acquire a permanent tie-breaker bonus. You then run through the second age — bidding, drafting, possibly grabbing heroes — then you tally your points.
I've played Nidavellir twice on a review copy, but only with two players each time which is a shame as the game will clearly play out differently based on the number of players. More players means more competition for the dwarves in each tavern, which means that bidding will be more important since you risk being locked out of the colors you need, whether for hero-worthy sets or for a points bonanza in a color. With only two players (or three), you draft more cards during the game, so you're more likely to complete ranks and get heroes, which means that scoring will be much higher than in games with four or five players.
In any case, I go further into the game in this overview: