This is an Akari, or Light Up, logic puzzle. The goal of this puzzle type is to light up every white square by placing light bulbs (or in this case, archers) into certain white squares. Bulbs light up entire vertical and horizontal rows, unless blocked by black squares, though they cannot be placed such that they shine on each other. Black squares may be labelled with a number. If so, that determines how many bulbs will be adjacent to its sides.
There are a few different approaches that will work for solving this particular grid. The most straightforward one begins by placing archers in the three squares surrounding the 3. Since there is an archer on the E, no archer may be placed on the S above it. Thanks to the nearby 2, we know that there must be two lights among the I, M, and N. However, the 1 tells us that only one of them may be on M or N; thus there must be a light on I. Following the trail of black squares up and to the right, the 1 tells us that since there must be an archer on either M or N, there cannot be an archer on either A or R, which tells us that the two archers for the next 2 must be on A and I. From here, the rest of the grid proceeds fairly simply by noticing which squares cannot contain archers and which squares must contain archers in order to be lit up.
At this point, we can read the squares with the archers from top to bottom, giving the clue phrase Robin Hood’s romantic interest, which gives the answer MAID MARIAN.