What exactly is the brew log used for?

I see it there in my Beer Smith sitting there all nice and empty.  Not sure how to best utilize this tool?

Pretty simple - the BrewLog interacts with the brewing calendar. After you do a brew - click on the recipe in the folder view that shows your various recipes - right click and select Copy. Now open the BrewLog and Paste the recipe in - open the recipe and make sure the date reflects the date of your brewing and hit OK.

The brew calendar will now reflect the times (days) you selected for Primary - Secondary - Bottle

I've used it in the past - have stopped - but will most likely start again as it can be a handy quick visual when you've got multiple batches going

I should mention that secondary is totally optional