To unbox something is to open it and remove it from its packaging. You'd better wait to unbox those birthday gifts until your actual birthday!
Use the verb unbox to mean "unpack" or "take out," especially when you're talking about a brand new item or one that's been mailed in an actual box. When you finally buy a new television, it will be exciting to unbox it. There is an entire category of internet videos in which people unbox electronics, toys, and other products, carefully documenting each stage of the process.