What is meant by "uneven spacing" on number line when dealing with floating point numbers in computers?
Let's look at a single-precision floating point number (as specified by IEEE 754). It is made up of 32 bits. Therefore, there are exactly $2^{32}$ floating point numbers that dots the number line.

What does it mean when we say that the floating point numbers are "unevenly" distributed on the number line? It means that they are not uniformly distributed. But why?

Well, let's consider the case where these numbers are distributed uniformly on the number line. Then there's some constant finite gap between successive numbers, $\Delta$. Since there are $2^{32}$ points on this line, then these uniformly distributed numbers span an interval of $\Delta \times 2^{32}$ width.

How big is $2^{32}$? Well, it's about 4 billion. Do you see the problem with uniformly distributed representations of numbers? If you want to even be able to represent the number $\pm 2$ billion in your uniform system, then you need to make sure that both $-2 \times 10^9$ and $2 \times 10^9$ are within your representable interval. Therefore, we need $\Delta \times 2^{32} \ge 4 \times 10^9$, so that we must space our numbers around $\Delta \approx 1$ apart. But if $\Delta \approx 1$, how are you going to represent both $1$ and $0.5$ precisely? Their difference is smaller than the gap!

Herein lies the rationale for having non-uniformly distributed representations such as floating point numbers. Uniformly distributed representations (or fixed-point numbers) cannot represent both big numbers and small numbers in a "good-enough" manner.