1. To keep a physical object in one's possession. When this usage is employed in informal situations, the phrase can end at "with." I always carry a pen and paper with me, in case I get an idea for a song when I'm away from home. Since you have a backpack, can you carry my book with?

2. To retain something abstract, such as an idea or feeling. I learned so much from my grandmother when she was alive and know that I will carry her sense of compassion with me for the rest of my life.