That is actually 2 bits appearing frozen together. The thingy with the clamp is the distributor advance arm, which attaches to the base of the distributor. The lower section is the distributor mount, which bolts onto the head and to which the advance arm attaches. The combination determines the ignition timing, and is therefore a big deal.
The mounts had a tendancy to break where the bolt hole for the head is, and might be hard to find as a result. The advance arms are fairly common. Need to be careful in getting one for a 52 or 3 Delco distributor, as the 51's tend to be autolite and don't interchange. There is a fix for broken mounts, but from your pic it may be too late.