The point of the game is pretty simple: you are trying to create one continuous line throughout the space that doesn't violate any of the constraints given to you. The space contains a grid of dots and some blank and numbered squares. The numbered squares tell you how many line segments surround the numbered space. With reason and deduction (and usually a crap-ton of time), you can determine the path of the loop.
It does take a while to get the feel of it, so if it's something you are interested in, start by reading the tutorial page, slowly increasing the size and difficulty, and making notes of tricks and patterns.
Now that I've gotten the trick of them, I race myself. My goal this week was to complete one of the 20 by 20s in under 15 minutes. This was my first success.
On the gargantuan weekly puzzle, like the one below, sometimes the easiest way to solve it is to step back and do something else for a while. Fresh eyes can really help when you are stuck. And I get stuck a lot.
I mean, these puzzles aren't anything special, but they are fun, they are free, and they make me feel like my brain isn't turning into complete mush.