Java - Building an Array of Objects using Scanner

Your main method doesn't do anything: it just contains declarations.

First case is to make an parametrized constructor for access to the private data- for writing

package stackoverflow.foo.sanctuary;

public class AnimalParametrizedConstructor {
    private String name;
    private String desc;


    public AnimalParametrizedConstructor(String name, String desc) {
        super();
        this.name = name;
        this.desc = desc;
    }

    //when no getters, that is the only way how to access to class fields for print outside
    @Override
    public String toString() {
        return "name: " + this.name + ", description: " + this.desc;
    }
}

Second way is to properly generate getters and setter for specific fields

package stackoverflow.foo.sanctuary;

public class AnimalGettersSetters {
    private String name;
    private String desc;

    AnimalGettersSetters(){
        //this is implicit constructor in java, you dont need to define it
    }

    public String getName() {
        return name;
    }

    public void setName(String name) {
        this.name = name;
    }

    public String getDesc() {
        return desc;
    }

    public void setDesc(String desc) {
        this.desc = desc;
    }   
}

Then you can call printing method from outside of the class anywhere you want (method must to be public), or to use getters for obtaining their values. For writing you can use parametrized constuctor in first case, or setters in second case.

Please, notice that you have to create new object instance in both of cases when you want to fill the array- AnimalParametrizedConstructor[] paramAnimals = new AnimalParametrizedConstructor[COUNT]; is just a declaration, not creating the instances (otherwise you will got nullpointer exception)

package stackoverflow.foo.sanctuary;

import java.util.Scanner;

public class SanctuaryMainClassWhateverName {

    public static void main(String[] args) {
        final int COUNT = 2;

        Scanner sc = new Scanner(System.in);

        // parametrized constructor section
        // load animals with parametrized constructor
        AnimalParametrizedConstructor[] paramAnimals = new AnimalParametrizedConstructor[COUNT];

        for (int i = 0; i < COUNT; i++) {
            System.out.println("What a name?");
            String name = sc.nextLine();
            System.out.println("What a description?");
            String desc = sc.nextLine();

            AnimalParametrizedConstructor newAnimal = new AnimalParametrizedConstructor(name, desc);
            paramAnimals[i] = newAnimal;
        }

        // and print them- because we defined toString, we have access to fields without
        // getter
        for (int i = 0; i < paramAnimals.length; i++) {
            System.out.println("animal no. " + i + ": " + paramAnimals[i].toString());
        }

        // animals with getter and setter section
        AnimalGettersSetters[] animalsGS = new AnimalGettersSetters[COUNT];

        for (int i = 0; i < COUNT; i++) {
            AnimalGettersSetters newGS = new AnimalGettersSetters();
            // load
            System.out.println("What a name?");
            newGS.setName(sc.nextLine()); // we have setters to private fields!
            System.out.println("What a description?");
            newGS.setDesc(sc.nextLine()); // we have setters to private fields!

            animalsGS[i] = newGS;
        }

        // print using gettes
        for (int i = 0; i < COUNT; i++) {
            System.out.println(
                    "animal no." + i + ": name: " + animalsGS[i].getName() + ", desc: " + animalsGS[i].getDesc());
        }

        // NEVER FORGET !
        sc.close();

    }
}

Honestly, you should to look for some OOP tutorials for beginning.