Yes, it's normal. Unless you're on a specialised connection, your upload bandwidth will be a fraction of your download bandwidth - hence sending information from your web browser to an internet server will be severely affected if you're uploading something in the background.
For simplicity, a connection sends data in packets, each packet when received has to acknowledge receipt of the packet and the integrity of said packet, so downloading will also utilise a small fraction of the upload of your connection so send the Packet Received OK or Resend Packet Damaged (to put it as simply as possible), so if you connection is saturated with uploading a video for example, this slows down your download speed as it has to queue the packet requests to sending server which then slows down the download speed of the connection.
Hope this helps answer your question. I can't think how to put it any simpler than this.