Transparent background
A transparent background means the picture has no coloured box behind it, so what is under it shows through.
In a simple example
A logo with a transparent background sits on a cream page or a green page without a white square around it.
Why it matters to you
It lets one logo file work on any colour.
Do not confuse with
Transparent is not white. A white box on a coloured page is the sign of a missing transparent background.