Life is
as a dream, it's not
a dream.
The major difference is that there are no other minds in your dream except your own mind
The expression "life is as a dream" is a bit misleading, because it tends to be misinterpreted as meaning "nothing is real, everything is illusion" (which is actually defended by some Hindu schools). This, however, is not completely correct: there is a conventional reality to life — we can all agree, for instance, that certain experiences and phenomena are common to all of us, and, therefore, we cannot reject their existence.
For example, we all agree that the sun shines during the day. What is different for everybody is how the experience of the sun affects each of us. Some might love the heat of the sun, others might feel the heat oppressive and hate the sun, most will be indifferent. So the sun, by itself, definitely exists, but its perception differs with the observer, and is definitely not the same for each person.
Similarly, what happens in our lives can be experienced in completely different ways, but it's foolish to reject those experiences as "illusions" or "dreams". For example, if we win the lottery, everybody around us might feel jealous (some will be happy, though!) and think that nothing could be better. But for us winners, it means that now we have an additional problem to deal with: how to protect the money, how to protect ourselves from hordes of "friends" who suddenly want to borrow some money or expect lavish gifts. So we cannot say that the event of winning the lottery didn't happen except in our minds — it definitely happened! — but the way we experience it depends upon our individual minds.
So why is "life like a dream"? Well, a dream is only experienced by the dreamer. What that means is that the experience of a dream is individual and unique, and while it can be described in detail to another person, it cannot be "shared", in the sense that the description, by itself, is not enough to evoke the
same dream on the other person. Now this seems obvious — the best that the other person can do is to
imagine the dream, based on its description, but they cannot experience
the same dream. It will be a
different dream! Even if the description could be accurate to the most infinitesimal detail, it would still be filtered by the perceptions of the listener, who would construct a slightly different mental image of that dream. No matter how much detail we put in the description, there is no way to replicate the experience
absolutely.
But the same happens to each and every experience in our lives! For example, imagine that I love women and watch a gorgeous blonde walking across the street. This evokes in me a certain image, tinted by my biased opinion about what a beautiful woman should look like. If I describe that blonde to a female, cisgendered, heterosexual friend, then she will create a completely different image in her mind. Why? Because my attraction to that blonde has a lot of feelings and concepts about those feelings attached to the blonde, while my heterosexual girlfriend will have different feelings and concepts. So the mental image she creates from the
same person will be different — it cannot be otherwise, since we are different persons. To put it bluntly: we create mental images of all that surrounds us and all that happens in our life, and, while that sequence of events that we call "life" is experienced by different people (not just myself!), their experience is totally different. Just like a dream, we cannot convey fully our experience of events happening in our life to other people: they will filter those events according to their own filters, perceptions, and ideas, just like they do with their dreams.
This is a bit more complex than it sounds, but I think that it's rather easy to see how different people view their lives (and all that happens in their lives) differently, because, well, they have different minds. So it's not like "life" is merely a collective hallucination and there is "nothing" out there. Rather, we know that there is "something" outside our minds because we can register how others react to the same events, so we know those events are real and existent. Nevertheless, we also know that every person sees each event in a slightly different way — or sometimes in a completely opposite way.
Life is definitely much more than merely a dream, but it shares the same attribute as the dream: the intangibility of the experience, which cannot be expressed in words, and which will be different from person to person.