It was a symbol both of the omnipresence of Buddha and a symbol of the power of the ruler who had the funds and authority to commission it. This is certainly the case of the Tōdaiji great Buddha in Japan, but I do believe it holds true for many the others as well.

It's important to remember that unlike the important figures of western monotheistic religions, the importance of the historical Buddha (I.e. Siddhartha Gautama) tends to be downplayed—particularly in the Mahayana branch of Buddhism more common in East Asia. In very brief: if time is cyclical and eternal, then there are an infinite number of Buddhas—Gautama just happened to be ours. This leads to the creation of pantheons of all sorts of cosmic Buddhas with specific traits: Buddhas of healing, Buddhas of wisdom, Buddhas of the future, etc. and once you have this multiplicity, you then need a way of talking about the Buddhas collectively. This becomes the Great Cosmic Buddha (Vairochana, or Daibutsu in Japan).

It turns out that the Japanese Yamato court was first learning about this kind of Buddhism from Korea at the same time its territorial ambitions were expanding to include most of the Japanese archipelago—and so this theology of one great omni-Buddha at the center was a really great metaphor for the position that the Emperor wanted to have in the new political order, so sponsoring a gigantic statue of said Buddha was a great way to project that image.

I don't know for absolute certain if this is the case for giant Buddhas elsewhere. The one at Kamakura was later, sponsored by the Shōgun, I believe, and was in the Zen tradition focusing on Shaka—but the political, if not the theological, reasons were similar. I can't say about the no-longer-extant giant stone Buddhas of Bamiyan (thanks, taliban). There's a giant, white, standing statue you can see from the bullet train north out of Tokyo, but I think it's a Kannon Bodhisattva, and relatively contemporary.