There are two basic ways of understanding the relationship between individuals in a group. The first way is individualism, which states that each individual is acting on his or her own, making their own choices, and to the extent they interact with the rest of the group, it's as individuals. Collectivism is the second way, and it views the group as the primary entity, with the individuals lost along the way.
Objectivism supports individualism in this sense. In a different sense, individualism is meant to be whether the individual is different from everyone else, or whether he makes up his own mind about things, or what-not. But in the individualist-collectivist sense of the term, individualism just means that the individual is a separate entity, making his own choices, thinking his own thoughts, and responsible for his own choices.
Collectivism views it in some other way. It sees the group as the important element, and individuals are just members of the group. The group has its own values somehow different from those of the individual members. The group thinks its own thoughts. Instead of judging the group as a bunch of individuals interacting, it judges the group as a whole, and views the individuals as just members of the group.
Collectivism might sound strange at first. I've known people who reject it as a straw man, a made up argument that's easy to attack. So let's give some reasons why people might accept it.
First, there's knowledge. Think about it in a few ways. First, how much of what you know did you learn from other people? That's taken to mean that nobody is truly an individual. Second, when coming up with an idea in a group, there's usually an exchange. It wasn't one person who invented the idea from scratch, but a group effort. So again, it's seen as the group that made the decision. Third, you're a product of your culture, right? Your outlook on life is at first very much dominated by the views of the people around you. If you're raised in a Christian home, you will very likely believe in Christianity.
Of course, the individualists sees this all in a different light. It's true you learned from others, but your mind had to grasp it. It's true that the invention took more than one person interacting to form, but each step along the way was made by individuals. It's true that you grow up within a culture, but you're free to accept or reject it. Being a part of these groups doesn't make you act the way you do. That's up to you.
Another reason for collectivism is the idea of mob mentality. When people are in a group, they sometimes stop thinking and just go with the wishes of their peers. Objectivists refer to this as second-handedness in a more general sense. But when someone is unwilling to think for themselves, and accept the wishes of the people around them, it looks and smells a lot like a collective. The only flaw is that the individuals are choosing to go with their peers, and they can also choose not to.
So do people actually view others in terms of collectivism? We need some examples.
An enormously significant example is that of racism. Racism is the view that there is a race of people, usually determined by skin color and appearance, and that they're all basically the same. Racism is fundamentally collectivist. Instead of viewing individuals by their own actions, values, or attributes, the group is judged and the outcome is arbitrarily assigned to the individuals. In other words, you get praised or blamed not by your own actions, but by the actions of someone else (or more than one person). This is a huge injustice, and turns the whole concept of moral judgment upside down.
There are other forms of collectivism. Any time where the group is considered to have a life of it's own outside of the individuals. An easy example is a nation. People often attribute qualities, values, etc., to an entire nation. And the nation often claims to have values that are different from the individuals.
Another example which I like to use but upsets some people is marriage. Marriage is often treated as a collective. This is why you hear things like "making the marriage work", as if it had a life of its own and the husband and wife are just there to satisfy it. What this example illustrates is that the collective need not be big. It's really a perspective issue. If you see the husband and wife interacting, then you can say things like "if you want to get along better, you should do this". But when the marriage becomes a value in itself, and the husband and wife are told to sacrifice in order to make it work, then they are acting as collectivists.
Ethically speaking, there are a number of problems with collectivism. For instance, because the collective is seen as having an importance higher than the individuals that make it up, those same individuals are asked to sacrifice for it. It is created into an intrinsic value, and destroys one's ability to rationally pursue one's own self-interest.
It also interferes with justice. Justice is concerned with making moral judgments about other people and acting accordingly. But collectivism destroys proper moral judgment by attributing value choices to the whole group, instead of the person making the choice.
Individualism is the proper approach to this problem. Moral judgments are made by moral agents. The person making the decision gets credit or blame for it. Values are agent-relative, and the person makes his choices by seeing how the value impacts his life. It is the individual that ethics is concerned with, and collectivism just obscures this point.