Pouring and carryingBulk trade amphoras held around 25+ litres, which, together with the weight of the clay they were made from, made them heavy to handle. The balance between one hand under the neck and the other under the pointed toe makes for very good control of the exact tilt of the jar while pouring. Greek vase paintings also show them carried over the shoulder by one handle, with the body supported on the shoulder, and the toe sticking out behind.
ShippingThe shape of the jars starts out (on the whole) more rounded with a smaller toe -- just a peg to serve as a handle -- in the early period (5th-4th centuries BCE) and gradually gets longer and thinner and more pointed through the Hellenistic period up until the 1st century CE. The shape was accommodated in shipping, both in actual ships, where the amphoras were nested between the ship's ribs and packed with branches to hold them in place, and on land, where they were slung in the saddlebags of donkeys, etc.
StorageBoth clay rings and wooden stands were used to support the jars by the lower body and protect the projecting toe. There is also evidence of amphoras standing in holes dug in an earth floor (in a wineshop in Pompey, for instance). The Greeks mixed their wine with water in a krater (big mixing bowl); once a kraterful of wine or two had been poured out of the amphora, it could be set down on the floor on its side and the shape of the rounded part of the body with its tapered lower end would raise the neck end so that the remaining liquid did not spill out.
StrengthIn excavations of ancient sites, whole amphoras are certainly found with the toe broken off, but many more are found with the toe intact and showing various degrees of wear. They seem to break much more easily across the lower body just below the maximum diameter. The toes are usually solid and the hollow part of the jar ends in a kind of ellipse shape at the bottom. This continuous curve gave them a much greater strength than a flat-bottomed design would, where the change in direction would be much more vulnerable to breakage. Some jars from Palestine, earlier than the Greek and Roman ones we study, have two handles without the pointed toe; but they also have rounded bases, so that they would not site on a flat surface; presumably this is because the rounded shape was stronger than a flat base would be. The Greeks did use flat-bottomed vessels for tableware (jugs and mixing bowls), and for bulk storage of goods like grain, wine, and oil (vats called pithoi), but shipping containers were pointed.
During manufacture, amphoras were not fired "to vitrification", so that clay was not brittle, but retained some resilience against being jostled in transit. The result was to leave the jars slightly porous, so that they sweat a little, which may actually cool them in local used, when the wine was drunk young. But jars usually had to be lined for export, often with beeswax, sometimes with resin or pitch. It is possible that retsina began this way -- the resin lining leant a piney taste to the wine -- but also possible that the wine was deliberately flavoured with resin to preserve it. Up until 1950 or 1960 one could see donkeys carrying goatskins of wine in the Greek countryside with pine branches sticking out of the top of the skin.
For bibliography on the handling of amphoras and their manufacture, see Physical characteristics of amphoras