Hi Anna,
We need to take a couple of steps back from the jargon here to the idea of classifications. We can classify things in a lot of ways, some of which will be generally meaningful to everyone (e.g. the novels of Iain Banks) versus subjective classifications (my favourite three Iain Banks novels). The first can be generally agreed upon and communicates information to others.
With organisms you can have a similar situation, but there are two aspects to classification. One part of this is being able to identify an organism and name it. This could use a variety of information and, critically, identification focuses only on being able to name the organism. Not tell us anything about the evolutionary of the organism. The other side of classification is systematics, how organisms are related to each other. This starts to come back to your question.
To cut a long story short, most evolutionary biologists and palaeontologists agree that our classifications should reflect the natural world as accurately as possible and take evolution in to account. The most powerful method we have devised for doing this is cladistics. One of the rules of cladistics is that the evolutionary groups we deal with (clades) must include a common ancestor and ALL of its descendants. Such groups are MONOphyletic. They reflect the branching off of particular evolutionary lineages and are terminated by the extinction of the last members of the clade. PARAphyletic groups include SOME but not ALL of the descendants of a common ancestor. In the case of invertebrates, we know that vertebrates share a common ancestor with invertebrates. So the concept of invertebrates as a group excludes some descendants and thus is not a valid grouping in these rules.
Another famous example is that if we try to separate out birds (Aves) then Dinosauria would be paraphyletic, as birds are a descendant of the same common ancestor.
The Wikipedia article has a useful diagram
http://en.wikipedia.org/wiki/Paraphyly