To drop someone/something off means you take someone or something somewhere and leave it/him/her there. For example: "I need to stop by the library to drop off a book before I get a late fee." OR "I am going to drop Jenny off at her school before I go to work."
To pick someone/something up means you go get it/him/her and take them with you. For example: Joe - "Do you want to go to dinner tonight?" Sara - "Yes, what time?" Joe - "I'll pick you up at 7." OR "Can you pick up some paper towels from the store on your way home?"
Hope that helps. :)