Adjectives are words that describe other words. They often give details about how something feels or looks. They can also give details about where something comes from (the origin of the thing) or how long something lasts or the length of something.
In the sentence "The American had long standing love for African birds", long and African are adjectives because they are describing other words, specifically the nouns in the sentence.
Long describes the length of the American's love. African describes the origin of the birds since they are from Africa. The other words in the sentence are not adjectives.