What is a brief announcement? What is a brief announcement in terms of accepted conference papers? 

For an example, see here
It is a short conference paper (maybe 2 pages) + a short talk (maybe 5–10 minutes).

Cf. a normal conference paper (maybe 10 pages) + a normal conference talk (maybe 20–25 minutes).

Brief announcements do not usually count as a publication, so you can use them to advertise work published elsewhere, or you can later submit a full version of your work to another conference.

In some conferences, you submit a normal paper, but if it is not quite sufficiently interesting to be accepted as a normal paper, it may be accepted as a brief announcement. In some conferences, brief announcements are a separate track — you directly submit a brief announcement. Some conferences combine both approaches: some of the brief announcements that they accept are "downgraded normal papers", while some of them have been directly submitted as brief announcements.