In biology and biological taxonomy, a clade is a group consisting of a single common ancestor, all the descendants of that ancestor, and nothing else. Over centuries of work, biological taxonomy has endeavored to split groups into clades, rejecting non-clade classifications, which are referred to as "paraphyletic." True clades are "monophyletic."
An example of a true clade would be birds. Birds are believed to all descend from a common ancestor that lived about million years ago. However, reptiles and apes are not clades. Reptiles aren't a clade because birds descended from reptiles (dinosaurs), and birds aren't considered reptiles. A group that excludes descendants of a common ancestor isn't a clade. Apes aren't a clade because humans descended from apes and humans generally aren't considered apes. If you include humans and the extinct relatives of humans, like Neanderthals, to be apes, then apes are a clade, but this generally isn't done.
Simpler organisms, such as arthropods (crustaceans, insects, millipedes, etc.) are more difficult to organize into clades, because there are fewer genetic and morphological features that can be used to determine common ancestry and ancestral lines. For instance, for decades in the late 20th century, scientists thought that arthropods (animals with external exoskeletons and jointed appendages) evolved on several separate occasions from soft-bodied ancestors such as annelid worms. Subsequent morphological and genetic analysis has found this to be false -- arthropods are indeed a clade, descending from a common ancestor that split from soft-bodied ancestors just once.
Determining clades at levels more specific than phyla can be challenging, especially for relatively simple animals. After decades of study, we still don't know how different arthropod groups are related to one another. Did land arthropods evolve from fairy shrimp, or some other group? We don't know for sure, and scientists are busy publishing papers and conducting analyses to find out.
Determining clades is difficult partially because much of the morphological and genetic data is ambiguous. Sometimes, a certain morphological feature -- like spines -- evolve via parallel evolution rather than manifesting in a single species and most (or all) of its descendants. Genetic data can be ambiguous because evolution occurs in different species at different rates, throwing off calculations that attempt to date time-of-divergence between species by comparing genetic commonality. To make matters worse, morphological specialists and genetics specialists tend to quarrel about the relative significance of their respective approaches. Correct determinations about animal clades only emerge after years or decades of in-depth research representing hundreds or thousands of papers and studies.