Existentialism is one of those topics that the more you try to pin it down, the more it refuses; at least that is my experience of it. There is no "quick" way to explain the philosophy, but Richard Appignanesi has provided an oft-tongue-in-cheek volume here that, I feel, acts as a suitable introduction. Granted, most of the concepts he doesn't go into any real great depth, but it should be enough of a taster to provide groundwork for further reading.
The book also examines how it is possible for one to have "bad faith", and engage in self-deception, especially when considering the absurdity of life. And there is quite a bit of discussion on how essentially awful our existence is, because it is limited, and because we are aware of our own incipient mortality.
So, we live life without hope of appeal, in what can be described as a series of "present" moments. Are we a ghost in the machine, an illusion of self? Existentialism may also be about the destruction of boundaries between this illusion and the world around it. Being is that which happens to us, a stream of flowing "nows", and it is limited by time. So how is it that we do not plunge into nihilism? Are we condemned to mean something, not be it?
What I gather is that one should return to a living experience as opposed to trying to structure existence by imposing meaning. Of course I could also be horribly wrong, and need to spend more time reading on the subject.