SIR PLZ ANSWER THE QUESTION IN SIMPLE WORDS
The evidence for an accelerating expansion comes from observations of the brightness of distant supernovae. We observe the redshift of a supernova which tells us by what the factor the Universe has expanded since the supernova exploded. This factor is (1+z), where z is the redshift. But in order to determine the expected brightness of the supernova, we need to know its distance now. If the expansion of the Universe is accelerating due to a cosmological constant, then the expansion was slower in the past, and thus the time required to expand by a given factor is longer, and the distance NOW is larger. But if the expansion is decelerating, it was faster in the past and the distance NOW is smaller. Thus for an accelerating expansion the supernovae at high redshifts will appear to be fainter than they would for a decelerating expansion because their current distances are larger. Note that these distances are all proportional to the age of the Universe [or 1/Ho], but this dependence cancels out when the brightness of a nearby supernova at z close to 0.1 is compared to a distant supernova with z close to 1.