This is just so that we can build computers and get them to do the things that we want. They are not doing anything for the computer. This is just a good method of programming into a computer to make sure that it operates the way that it should operate.
Indents are very important for readers, just like paragraphs are and line breaks. You need to break up the text in certain ways, otherwise it becomes very hard to read and you want to give up on even trying. Indents make the reading experience much more pleasant. It's for the reader.
Indent style is really for the benefit of people who are reading computer programs. Computers do not need a specific style such as this to work effectively. Indent style allows users to read more clearly and make sense of convoluted code by pre-programmed spacings. Computers can read code as long as it has the right symbols and terms in it.
For computers, it simply does not matter if code is smashed together or not. Indent style was originally used to make it easier for programmers to read the code. It can not be used as a way to format programs as well, so it can now affect how a program runs. Overall, I would say that it is in existence so humans can read the code more easily.
While indents provide a visual separation that makes it a bit easier to follow long lines of code, machines will also use the indent markers as indications. The computer just reads them different from how humans do. This is also dependent on the language in which the code is written. C++ for example does not recognize indents. They are still available for ease of human use.