Traditionally, Keywords used to be the only target option for manual campaigns. Targeting keywords will have your sponsored products appear in Amazon's search results when a customer enters the respective searchterms.
Keywords can be set to broad, phrase or exact, depending on your ad group'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 average rating, so that you can have your sponsored products appear for searches with specific filters, e.g. kitchen category, price between $10 & $30 & rating better than 3.
At this time (manual) ad groups can only target either Keywords or Product Targets.