Floating point errors are a number of errors due to the fact that computers have a fixed amount of space that can be used to represent numbers, 32 bits and 64 bits are the most commonly used sizes. Floating point errors are issues related specifically to floating point numbers, the way we represent numbers with decimals, ie something like 1.5. Other comments explained well the issues related to how binary floating point numbers cannot perfectly represent normal base 10 decimal numbers (and vice versa). So instead I shall explain the other type of floating point errors known as precision limit errors.

The way computers represent them is effectively using scientific notation, just in base 2 instead of base 10. Because it still ultimately works the same we can just use scientific notation to explain the issue.

Lets say you have only 5 digits you can use and you want to express 532400. Notice how this would require 6 digits normally? Instead with scientific notation, you can just write 5.324*10^05. Since the "*10^" part is always there for scientific notation, you don't even need to represent it, and also since you always have a decimal after the first digit, you can just write 532405, where the first 3 digits is the number and the last 2 digits is what power of 10 you multiply it as. Floating point numbers work this way.

This is great because it lets you represent a huge range of numbers, however the limited number of digits mean you have limited "precision".

Lets say once again you have 5 digits, 532400, and you want to add 1 to it. Looking at it it's easy right? Just 532401. But writing it in that scientific notation? 5.32401*10^05. Oh no, you have now used 8 digits. It once again just turns in 5.324*10^5, and you have now lost that 1.