In Java 8+, use StringJoiner:
public String getDescription() {
    StringJoiner description = new StringJoiner(" & ");
    if (line.contains("A"))
        description.add("Apple");
    if (line.contains("B"))
        description.add("Banana");
    if (line.contains("C"))
        description.add("Carrot");
    return description.toString();
}
In Java 5+, use StringBuilder and if statements:
public String getDescription() {
    StringBuilder description = new StringBuilder();
    if (line.contains("A")) {
        description.append("Apple");
    }
    if (line.contains("B")) {
        if (description.length() != 0)
            description.append(" & ");
        description.append("Banana");
    }
    if (line.contains("C")) {
        if (description.length() != 0)
            description.append(" & ");
        description.append("Carrot");
    }
    return description.toString();
}
Or, as pointed out by kaya3:
public String getDescription() {
    StringBuilder description = new StringBuilder();
    String sep = "";
    if (line.contains("A")) {
        description.append(sep).append("Apple");
        sep = " & ";
    }
    if (line.contains("B")) {
        description.append(sep).append("Banana");
        sep = " & ";
    }
    if (line.contains("C")) {
        description.append(sep).append("Carrot");
        sep = " & ";
    }
    return description.toString();
}
Or the way the question code is trying to do it:
public String getDescription() {
    StringBuilder description = new StringBuilder();
    if (line.contains("A"))
        description.append("Apple & ");
    if (line.contains("B"))
        description.append("Banana & ");
    if (line.contains("C"))
        description.append("Carrot & ");
    if (description.length() != 0)
        description.setLength(description.length() - 3); // remove final " & "
    return description.toString();
}
Test
System.out.println(new VeggiesAndFruits("").getDescription());
System.out.println(new VeggiesAndFruits("A").getDescription());
System.out.println(new VeggiesAndFruits("B").getDescription());
System.out.println(new VeggiesAndFruits("C").getDescription());
System.out.println(new VeggiesAndFruits("AB").getDescription());
System.out.println(new VeggiesAndFruits("AC").getDescription());
System.out.println(new VeggiesAndFruits("BC").getDescription());
System.out.println(new VeggiesAndFruits("CBA").getDescription());
Output (same for all 4 solutions above)
Apple
Banana
Carrot
Apple & Banana
Apple & Carrot
Banana & Carrot
Apple & Banana & Carrot