This puzzle is a Star Battle, which is an elegant and easy-to-learn puzzle type. All you have to do is place some stars into the grid such that exactly one star, (or more stars for larger puzzles), appears in each row, column, and bold region. Also, no two stars can be placed in adjacent cells, not even diagonally.
For the puzzle I published today, I took a couple of steps beyond the basic Star Battle formula. First, I made the grid quite large, (15x15 with 3 stars per row/column/region). Then I also provided two grids. Each grid has the same solution of stars, so you work back and forth between the grids to solve them both simultaneously. Finally, instead of dividing the regions into random-looking arbitrary shapes, I tried to make some recognizable pictures with the grids. If you click through above, hopefully you'll be able to recognize the shapes I was going for. This puzzle marks my first in a series of puzzles where I chose the name of the puzzle type as the theme for the puzzle. So, I drew a star battle for a Star Battle puzzle. And with dual grids, I named this battle a Star Duel.
Finally, I should point out that where my previous puzzle was published on a Monday, today's puzzle is published on a Saturday. The GM Puzzles website publishes puzzles that get increasingly difficult throughout the week. So if you've never attempted a star-battle puzzle before, I don't actually recommend you start with my puzzle from today.
Instead, you might start with this simpler star battle puzzle that I wrote as part of a Christmas puzzle hunt for my boys. It's a very gentle introduction to the puzzle type. If you try it, you can ignore the second grid with the C, H, A, and S regions. That was part of a metapuzzle included in the puzzle hunt.