This game is a casual, low pressure puzzle game, where the goal is to place pieces (buildings, etc) on a procedurally generated island to score points, and try to score as many points as possible before running out of pieces.
You start by drawing a few pieces. You can place them freely, and you have to meet a certain amount of score before you can draw more. As long as you keep hitting that score, you can keep drawing more pieces. If you run out of pieces, it's game over.
The points you score depend on the synergies with other buildings and features of the island (trees, etc). For example, a lumber mill will score one extra point for each tree nearby, but will lose points if there are other lumber mills nearby. There are dozens of buildings and synergies to explore.
After a certain number of points, you can leave the current island and a new empty one will be generated.
This game compares well with Dorfromantik (also a great casual game, btw). Islanders is slightly less polished and the graphics are more basic and controls are a little bit clunkier, but that does not detract from the fun.
There are only two real downsides to Islanders, IMHO, but these are minor. First, sessions tend to be very, very long, because if you "play to win", you can aggressively leverage placement mechanics to score massive points and stay alive for ages, and then strategically bail out of the island once scoring becomes hard. This resulted in multi-hour sessions for me (thankfully, you can save the game and continue later).
The other downside is that your creations are ephemeral. Because they don't persist, so you will probably care less about aesthetics. I found myself making ugly clumps of buildings just for the score, whereas in Dorfromantik I cared (probably way too much) about aesthetics. It is not bad, just different.
Islanders is still a solid game on its own merits: a unique and nice casual game that won't wow you, but will put a smile on your face.