The file is called ldwLog.txt and is located in the Virtual Villagers folder, and it can be viewed easily in any text editor (such as Notepad or WordPad). When viewing the game log, you can see when villagers have been injured, or have lost health due to disease, old age, or starvation. You can also see when villagers have mated and with whom, and the production of food and tech points.

The game log is overwritten each time you launch the game, though, so it has to be viewed immediately after you quit the game.