Object is the noun on which the action (I.e verb) is applied.
Eg: I eat an apple
The action is "eat". What is the thing that you are eating? Apple. So "apple" is the object.
An adjective is a word that describes/gives more information about a noun. Eg: red book. The "book" is the noun, and can you describe the book? It is red, so "red" is the adjective.
Before you get into noun phrases, understand what a phrase is.
A phrase is simply a group of words that form a part of a sentence, for example, ‘in the dark night’ or ‘within the bustling crowd’. There is no verb, so a phrase cannot be a complete sentence.
Now for a noun phrase.
A noun phrase is a small group of words which contains a noun but doesn't contain a verb. Basically, a phrase for which the main word is the noun. A noun phrase usually contains a noun plus other words to describe it. These words could be adjectives, articles, prepositions, anything except verbs.
Example: That new pink bike is mine.
In this sentence, ‘that new pink bike’ is the noun phrase. ‘Bike’ is the noun, and the other words describe the bike.