'Bandwidth' describes the rate at which data can be transferred to your computer from a website or internet service within a specific time. Therefore the amount of bandwidth you have (the bandwidth 'strength') determines the efficiency and speed of your internet activity – that is, when you open web pages, download files and so on.
A useful analogy is a pipe with water running through it – the wider the pipe, the greater the volume of water that can flow through it. The same applies to bandwidth strength and the flow of the volume of data.
Bandwidth is generally measured in ‘bits per second' or sometimes ‘bytes per second'.