Binary numbers are written in base 2. Each digit is either a one or a zero. The least significant digit is the units column, building up to the most significant digit being 2 to the power (n-1) where n is the number of digits. Each binary digit is called a bit. In 8 bits you can store values from 0 (all 8 are 0) to 255 (all 8 are set to 1) and all values in between.
E.g.
Write some code that will translate a number into binary and then light up the lights so that led 1 represents the least significant bit (i.e. the units) and led 8 the most significant bit (i.e. the 128s).
(Debug hint: output the current value over the serial connection when the button is pressed.)
Thinking back to the Ex4_7_PotBarGraphprogram. Copy that and amend it so that rather than lighting a single led, instead the value (from 0 to 1023) is mapped into the range 0 to 255 and then the appropriate binary value is displayed.