Traditionally, Keywords used to be the only target options for manual campaigns. Targeting keywords will have your sponsored products appear in Amazon's search results when a customer enters the respective searchterm.
Keywords can be set to broad, phrase or exact, depending on your adgroup's goals (keyword research vs milking proven keywords).
Product targets consist of ASIN & Category targets.
ASIN targets will have your sponsored products appear on the listing pages of competitor ASINs.
Category targets can be refined by product category, price or avarage rating, so that you can have your sponsored products appear for searches with specific filters, eg. kitchen category, price between 10$ & 30$ & rating better than 3.
At this time (manual) adgroups can only target either Keywords or Product Targets.