It's easy to think about floor and ceil from the perspective of the number line. Let's say you have some decimal number, $2.31$ ^{(I'm going to be using this number as an example throughout my answer)} $\hskip2in$
So, as you can see, the functions just return the nearest integer values.
floor returns the nearest lowest integer and ceil returns the nearest highest integer.

All real numbers are made of a characteristic (an integer part) and mantissa (a fractional part) $$\text{Number} = \text{Characteristic} + \text{Mantissa}$$ $$2.31 = 2 + 0.31$$

When floor a number, you can think of it as replacing the Mantissa with $0$ $$\lfloor 2.31 \rfloor = 2 + 0 = 2$$

and ceil can be thought of as replacing the mantissa with $1$. $$\lceil 2.31 \rceil = 2 + 1 = 3$$

That's not a very popular way of thinking about it but it was the way I thought about it when I first started using it in programming.

Remember, the number remains the same when it is an integer. ie, floor($3$) $=$ ceil($3$) $= 3$

Let's now look at the proper definitions along with the graphs for them.

Floor Function: Returns the greatest integer that is less than or equal to $x$ $\hskip2in$

Ceiling Function: Returns the least integer that is greater than or equal to $x$ $\hskip2in$

Don't let the infinite staircase scare you. It's much more simpler than it seems. Those "line-segments" that you see are actually called piecewise-step functions.

Simply, the black dot represents 'including this number' and the white represents 'excluding this number'. Meaning that each segment actually is from x to all numbers less than x+1.