getting an object from an arrayList with objects attribute

Just implement the equals method in the class Klass1.

public class Klass1 {

    String bir;
    String myID;

    Klass1(String bir, String myID)
    {
        this.bir=bir;
        this.myID=myID;
    }

    public boolean equals(Object o){
        if(o instanceof Klass1)
            return ((Klass1)o).myID.equals(myID);
        else
            return false;
    }

}

Its because you are trying to delete a new object which isnt in the arraylist. When you use new klass1("vz","45") you are creating a new instance of this class which isnt in the arraylist.

What the system does internally is to compare those classes using equals. Why this doesn't work is explained in the following code:

Object o1 = new Object();
Object o2 = new Object();
System.out.println(o1 == o2); // false, obviously
System.out.println(o1.equals(o2)); // false
System.out.println(o1); // java.lang.Object@17046822
System.out.println(o2); // java.lang.Object@22509bfc

You can tell by the number following the @ that these objects have a different hash values, and this is what the equals function of Object does check.

This is relevant for your klass, because unless you overwrite equals, you will use the equals of Object. And if you implement equals you should always implement hashcode as well. Because both tell you something about whether or not two objects are the "same", and if the one says something else than the other, some part of your code might get confused.

How to properly implement equals for your class:

@Override
public int hashCode() {
  int hash = 7;
  hash = 17 * hash + Objects.hashCode(this.bir);
  hash = 17 * hash + Objects.hashCode(this.myID);
  return hash;
}

@Override
public boolean equals(Object obj) {
  if (obj == null) {
    return false;
  }
  if (getClass() != obj.getClass()) {
    return false;
  }
  final klass1 other = (klass1) obj;
  if (!Objects.equals(this.bir, other.bir)) {
    return false;
  }
  if (!Objects.equals(this.myID, other.myID)) {
    return false;
  }
  return true;
}

This can be done in most IDEs btw with a shortcut (i.E. alt-insert in Netbeans). Note that I did this in Java 7 using Objects. If you are in Java 6, you need to manually type
(a == b) || (a != null && a.equals(b)); with the appropriate objects to compare.

Creating a proper hashcode is not always trivial, for more complex objects you might want to read a bit about hashcodes first. For simple objects: multiply primes with something.

The equals method is usually trivial, it is just important to first check for null and for class equality. This is often forgotten by programmers and a common source for NullPointerExceptions and ClassCastExceptions.