Why is it important to determine the wavelength of maximum absorption?
I assume we are talking spectroscopy here?
When describing the spectrum it is usual to record the wavelength of a maximum absorption (there may be several absorptions) as this is a characteristic of the material. This is a piece of information that another reseacher could use to identify a compound that they have. There is no point in recording the wavelength of a slope of a curve as this is difficult to identify by another researcher as to where you are referring to on their slope. Sometimes other features are recorded, say the mimimum where two peaks overlap.
In essence the peaks are reproducible and identifible.
Does this help?
Another item to add to DrRuss' excellent answer is that the maximum wavelength often is used for quantitative work and the maximum needs to be identified because that is the point of maximum sensitivity for the material being measured.