Hi is a casual way of saying hello,  and also, the homonym of high.

Hi was first recorded as being something one person said to another upon seeing them back in the days when Middle English was spoken.

Middle English? 

Middle English is the name given to whole variety of English dialects spoken in England from 1100 to 1470. it wasn't a single language at all! So what happened in 1470 to change all that?

In 1470, William Caxton brought the printing press to London and people began printing things using a single type of English spelling and grammar called Chancery Standard, which was used in London chanceries, or writing offices; this was a time when few people could read or write, so official papers were recorded, by hand, by secretaries or chanceliers. The printers imitated the letters and usage of the chanceries and pretty soon this official language spread over the country and became the dominant one.

Here's a sample of how this beautiful form of our language looked:

Wow! Wonder if there's a "hi" in there somewhere?