Its an idea that relates to how we can indefinitely count in "both directions". In other words we can count in whole steps forever, we can also do the same for the space between the steps.
Consider a ruler, we can count the 12 inches that are clearly marked out and we can count out all the lines in between the inch markings. We can keep dividing and we can imagine the idea of doing this indefinitely. Of course physical limitations will only allow us to divide things so far down.
There really are no paradoxes. These infinitesimal brain teasers rely on how the terms are defined. In other words how the sets of the mathematical system are described. Real Numbers represent the set of all numbers including fractions, decimals, and even whole numbers. This 'set' includes all the other 'sets'. A natural number is the basic 1,2,3,4 etc (or 0,1,2,3 etc). A real number would include pi or 3.3333333 or 1/5 or 1/3 etc.
The idea is that there are more real numbers than natural numbers even though both are 'infinite'. The thing is infinite means boundless. What counting means is we can count forever. The supposed paradox here has to do with confusing numerical symbols and concepts with the quantities they are supposed to represent. These quantities can be real or imagined. These quantities are things like the dimensions of a physical object or its weight, the amount of gas in your car or the amount of debt ( represented by a negative number) you owe.
The sleight of hand of this supposed paradox is the confusing of the numerical symbols and concepts with the quantities they represent. Math simply involves counting of one kind or another and the whole numbers work with the rest of the sets of numbers of the system just fine. The whole system is one numerical system and any divisions are very arbitrary in terms of making metaphysical claims of cosmic mystery paradoxes. (cosmic means order)
We can also simply convert 3.33333 to 333,333 like the metric system allows and we will have only whole numbers and no fractions. We just scale down or up. We can go to nanometers or smaller and we can go to kilometers or bigger. We do not have to resort to fractions. We can extend pi out as far as we like, 3.14159 etc can become 314 or 3142 (rounded) or 314,159 etc. We have to round pi off at some point and all this shows is the limits of math as a human tool. We only need to know what resolution we need and that is our limit. In the real world we can only measure sup to a certain 'resolution' anyway so we are physically limited from truly dividing something down indefinitely.
We can also convert whole numbers to decimal placed numbers by adding as many zero placeholders as we like: 1 becomes 1.000000000 etc.
"Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. In fact, Cantor's method of proof of this theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware."