"Download speed" refers to how quickly a file can be downloaded from a remote source. To "download" something means to obtain it on your computer, usually through the internet. This is usually from a website that has the file that you want, or, it can be from another user that allows you to download the file directly from them. So,, the download speed is measured by how much of the file is transferred to you over a certain amount of time.
Most download speeds are measured in "kb/s", which stands for "kilobytes per second".
A kilobyte is 1000 bytes, and a byte is in turn made up of 8 bits.
The download speed of a file is dependent on how much bandwidth both the downloader, and the uploader, that is, the on e providing the file, can use in the download.
"Bandwidth" is a measure of the available resources your internet connection has available to use in downloading files.
Bandwith is usually measure in either "kbits" or "mbits", which stand for thousands or millions of bytes of resources respectively.