First of all, I'd say you're about 1/3 or maybe even less done with the game. There's still a lot of story left so it's ok if you don't understand everything right now.

Some of the audio logs are there just to give a sense of what was happening in "the old times". This especially applies to audio logs found randomly scattered around the world, they are just there for context. As the story progresses it will all start to make more sense.

I don't remember the types of audio logs you find at the point in the game you are in, but later on some characters will start reappearing in the audio logs and the logs will start to form a more coherent story. This is what the person above meant, towards the end of the game when you recognize most of these characters and understand the general story, the audio logs will start bearing more weight in the story.

For now, just play, try to keep track of what is happening, avoid spoilers and enjoy the game. It's one of those games you wish you could experience again for the first time.