Mbps is an abbreviation for megabits per second.
Megabits per second measure the speed that data can be passed through your internet connection. In other words, it's the speed that web pages take to load when you're surfing the internet, or the speed that something takes to download.
There are eight bits in a byte so 1 Mbps is equal to 0.125 MB/s or megabytes per second. For example a download of a 4 MB music file on a 1 Mbps internet connection would take 32 seconds.