The short answer is that miacids are a now extinct group of small carnivores.
In the early Tertiary period (about 55 million years ago as I write this in 2004 AD) after the extinction of the dinosaurs, many new species of mammals appeared to take advantage of their absence. One of the new orders of mammals that began to appear about this time is Carnivora, which includes most of the modern carnivorous land mammals such as cats, dogs, bears, weasels, etc.
The miacids are sometimes cited as being the common ancestor of either all of order carnivora, or at least the common ancestor of the cats (felids) and dogs (canids). There is some question about whether this is really true as the details of the family tree are still kind of murky. Several authoritative looking web pages I found seem to suggest that the miacids actually swing a little closer to the dog side of the family. In any case they were certainly in on the whole carnivore thing near the beginning.
The San Diego Natural History Museum has a nice fossil skeleton of one (unusually large) species of miacid. This link shows the skull and a nice artist's conception of one lurking in a tree.
Here is another artist's impression.
And finally, here is a description of a columnist for a local (to my home town of Portland Oregon) newspaper being killed by a miacid while playing a computer game. Since I rather like miacids and I'm generally unimpressed by the Portland Mercury, I take some small pleasure in this.