The download speed is how fast data can be received from the Internet to you. Connections are usually designed to download data much faster than it is uploaded. This is because the majority of online activity (such as loading web pages or streaming videos) consists of downloading data.
The upload speed is how fast data is sent from your location to others. Fast upload speeds are necessary for sending big files via email or when using applications like video chat. Faster upload speeds help ensure smooth motion and good picture quality for the person you're talking with.