Something elephantine is huge, bulky, and a little clumsy, much like an elephant. Riding a bicycle in a rainstorm while trying to hold an elephantine super-sized soda is a bad idea.
An elephant is one of the largest animals in the world — even the babies weigh more than most people! So, things that are also enormous can be called elephantine. Other big animals — like whales — are elephantine. A cake that could feed fifty people is elephantine. If you owe a lot of money, that’s an elephantine debt. Elephantine things can also be unwieldy and bulky or just plain huge. Anything elephantine is extra-large.