Tao

I just had to attempt to define the Tao as person, place, thing, or idea. Lao Tzu would be furious with me right now. The Tao is the nature. The ultimate thing that contains all opposites. The thing that is greater than good vs evil or reality vs illusion. Accepting the tao gives peace by placing one above all conflict.
That which can be Defined is not the Tao

Dao. Mostly associated in the West with Daoism and the DaoDeJing, it is a Chinese word with many meanings. Originally, the basic meanings are "road" and "woof" (as is the warp and the woof, or weft), signifying the horizontal lines of a fabric or a system of roads and paths. In contrast to "jing". Dao has come to mean many things, including road, way, path, morals, origin, line, journey, way or method, course, or doctrine. Used by the Daoists to indicate that which is common to all things. Similar in some ways to Zen, although very different in their linguistic roots (Zen is a bastardization of the Sankrit "Dhyana", by way of the Chinese word "Chan", all of which refer originally to deep meditative absorption, but have come to refer, in English to some peculiar quality that is difficult to name. In the DaoDeJing, it is referred to as the source of all things, mother of the universe, so large that it contains all, and yet so small that nothing is not permeated by it. The classic analogy, used also in Zen circles, is that of a the fish who does not know what water is because it is all pervading, and yet it is precisely that which gives life. (spelt Tao in the Wade-Giles system)

Tao (in Wade-Giles romanization, which is misleading in terms of representing pronunciation) or Dao (Pinyin) means many different things. In Chinese language and culture it is ubiqitous, primarily because its bandwidth of meanings is so large and vague. It's fundamental meaning is that of a "way" in the sense of a "way of" doing or knowing or behaving or speaking of something. Christian missionaries used "dao" for "logos" in their translations of the Gospel of John. Thus, "In the beginning was the Dao. And the Dao was with god..."

Many contemporary constructions of Taoism (or Daoism) bear little or no relation to previous historical versions. Which is not necessarily a bad thing. Sometimes these are naive, sometimes much more profound those that came before.

When a superior man hears of the Tao,
he immediately begins to embody it.
When an average man hears of the Tao,
he half believes it, half doubts it.
When a foolish man hears of the Tao,
he laughs out loud.
If he didn't laugh,
it wouldn't be the Tao.

- ch. 41 Tao Te Ching

The verb in the first line of the Tao Te Ching (translated by Stephen Mitchell and others as 'The tao that can be told is not the eternal Tao,' as above) is actually tao, which can mean 'express' as well as 'travel' and 'way': 'The tao that can be taoed is not the eternal Tao', if you like. A wide variety of translations are therefore possible - I have seen 'The path that can be travelled is not the eternal Path', for instance, which is a plausible literal translation but probably misses the point of what Lao Tzu was trying to say.

The word Tao/Dao has made its way into Japanese and Korean as do, or doh; this is often found in the names of martial arts, where it is best translated as 'way' - take Aikido (Japanese) and Tae Kwon Do (Korean), for example. In Japanese, it is contrasted with jitsu or jutsu (Chinese shu), meaning (roughly) 'techniques' or 'craft'; compare judo and jiu-jitsu, aikido and aiki-jutsu, and so on.

Another fun fact about the word Tao is that the character is composed of two others, roughly translating as 'halting steps' and 'forward' - which gives neat little glimpse into how Taoists see things working.

In Unicode Chinese characters, the opening of the Tao Te Ching looks like this, reading top to bottom then left to right (unless it's mangled by your browser):

        名     道 
        可     可 
        名     道 
        非     非 
        常     常 
        名     道