Basically, information hiding is about code clarity. It's designed to make it easier for someone else to extend your code, and prevent them from accidentally creating bugs when they work with the internal data of your classes. It's based on the principle that nobody ever reads comments, especially ones with instructions in them.
Example: I'm writing code that updates a variable, and I need to make absolutely sure that the Gui changes to reflect the change, the easiest way is to add an accessor method (aka a "Setter"), which is called instead of updating data is updated.
If I make that data public, and something changes the variable without going through the Setter method (and this happens every swear-word time), then someone will need to spend an hour debugging to find out why the updates aren't being displayed. The same applies, to a lesser extent, to "Getting" data. I could put a comment in the header file, but odds are that no-one will read it till something goes terribly, terribly wrong. Enforcing it with private means that the mistake can't be made, because it'll show up as an easily located compile-time bug, rather than a run-time bug.
From experience, the only times you'd want to make a member variable public, and leave out Getter and Setter methods, is if you want to make it absolutely clear that changing it will have no side effects; especially if the data structure is simple, like a class that simply holds two variables as a pair.
This should be a fairly rare occurence, as normally you'd want side effects, and if the data structure you're creating is so simple that you don't (e.g a pairing), there will already be a more efficiently written one available in a Standard Library.
With that said, for most small programs that are one-use no-extension, like the ones you get at university, it's more "good practice" than anything, because you'll remember over the course of writing them, and then you'll hand them in and never touch the code again. Also, if you're writing a data structure as a way of finding out about how they store data rather than as release code, then there's a good argument that Getters and Setters will not help, and will get in the way of the learning experience.
It's only when you get to the workplace or a large project, where the probability is that your code will be called to by objects and structures written by different people, that it becomes vital to make these "reminders" strong. Whether or not it's a single man project is surprisingly irrelevant, for the simple reason that "you six weeks from now" is as different person as a co-worker. And "me six weeks ago" often turns out to be lazy.
A final point is that some people are pretty zealous about information hiding, and will get annoyed if your data is unnecessarily public. It's best to humour them.
