Euclid was a Greek mathematician who lived around 300BC (about 2300 years ago), and who is often referred to as the “Father of Geometry”. He collected all the geometrical proofs and results existing at his time into a monumental work, called the Elements, which contained thirteen books. These books had an extraordinary impact on later generations, and the geometry you will be studying over the next few years is all based on Euclid’s original effort. In a sense, one can say that Euclid was one of the most influential humans who ever existed.
What do we mean when we say “Euclid’s Geometry”? The geometrical ideas put forth by Euclid are so natural, so appealing to common-sense, that for a long time (more than 2000 years) people thought that whatever Euclid wrote (or the geometrical system he constructed) was the ultimate truth.
Only in the last 200 – 300 years did mathematicians start realizing that Euclid’s Geometry may not be the final truth. They discovered other kinds of geometries, in which the results of Euclid do not hold at all. The most surprising aspect of it all is that the universe we inhabit does not have a Euclidean Geometry, even though to the human mind, it seems that way (because our brains are wired that way, and because world over, when students start studying geometry, they start with Euclidean Geometry – the way you have done!).
These are deep ideas, which you will only start understanding over a longer time. For now, remember this: Euclid’s Geometry is one particular system of geometry; it is not the only system of geometry.