Question

What is axioms ?
Thanks in advance

Answer 1

All mathematical reasoning is founded on simple principals, the truth of which is so evident that they are accepted without proof. These self-evident truths are known as axioms.

In simpler words, some theorems in mathematics require no proof to prove its accuracy. Their truth is that much obvious. They are axioms.

For instance-

If two numbers (let $x$ and $y$) that are equal to each other ($x=y$ ) are added to the same integer (let $z$), the sums will be equals.

This statement is self-explanatory. 
$x+z=y+z$

The above equation represents the theorem. You do not need a proof to be assured it's 100% correct. It's quite obvious. Some things don't need explaining and they're AXIOMs!