Okay, imagine you're on a really long car ride with your parents. You're driving to a really cool amusement park, but the road to get there is really bumpy and sometimes it's hard to see where you're going.
"Stay the course" means that you should keep going in the same direction, no matter how bumpy or hard it seems. Even if it feels like you're lost or you're not getting closer to the amusement park, you trust that your parents know the way and they will get you there eventually.
In life, "stay the course" means that if you have a goal or a plan, you should keep working towards it, even if it gets tough or you're not sure if you're making progress. Just like in the car ride, it can be hard to see the end result, but if you keep going and don't give up, you will eventually reach your destination.