To rouse someone who's sleeping is to wake them up. Your parents might rouse you before dawn to get ready for school. Or, maybe you're roused by the delicious smell of biscuits cooking, or maybe you're roused by the sound of your siblings running around or playing music. Here's Patrick, roused by the sound of his alarm clock.
Often we rouse someone from their sleep, but we can also rouse someone who's not paying attention. In that case, to rouse people is to catch their attention and make them focus. If your friend is daydreaming in class, you might have to rouse her from her daydream.
Lastly, if you call something rousing, you mean it's exciting, like it has the power to wake people up, grab their attention, and get them moving. A rousing cheer or a rousing song is a loud, exciting one that makes people join in. Here's King Bob giving a rousing speech.