The Today Tab shows stories from the channels you follow, organised by topic and the day's biggest news.
Right at the top of the page is the "Top Stories" stack. You can move through the stack by swiping left or right.
Long pressing on a story brings up the story menu. Here you can bookmark a story for later or share it with others.
As you scroll down, you'll see stories sorted by topic. Big News intelligently scans the contents of each story and organises them into distinct categories.