Uploads and downloads affect your monthly quota. Depending on what plan you're on, the amount you can upload and download is different.
A download is everything you receive over the internet. That means even just viewing a web page is counted as a download. When you save videos from a website onto your computer, or stream a Youtube clip, that's also a download. Even when you open an email you are downloading.
An upload is the opposite to a download. It's when you transfer a file from your computer onto the internet. If you use a webcam or play online games, these are also classified as uploads. When emailing people, the email leaving your computer is an upload. If you're prone to sending around lots of photos to your family and friends, check how large the email file size is before sending both to be courteous to your receiver's quota limits and to also limit any effect uploads will have on your own quota.
For more information about uploads and downloads and how they affect your quota, visit the iiHelp article all about quota and shaping