It is quite controversial whether slides are better than a board, and I think this also depends very much on what and how you are teaching. But you have asked specifically for advantages, so I will try to focus on those. I will, however, mention caveats.
As Shawn says, slides can work as a very nice conceptual map of where you want your lecture to go, compared to just going up to an empty board with a chalk. The caveat is that you can simply prepare a few sheets of handwritten notes, and use these to accomplish the same goal.
It is much easier to pace yourself, both because the slides serve as a detailed outline and also because you can use the number of slides as an estimate of how long you will take. (but this can also be done by preparing notes, counting the pages or doing a practice lecture with a stopwatch)
You can return to previous slides easily or peek ahead as needed without having to erase the board and re-write everything.
There is no risk of students having trouble reading your script (unless your slides are truly pathological), everything is clear. Of course, you could just write legibly.
Typing is faster/less tiring than writing for many people. Perhaps it takes you 50 minutes to type up everything on the slides you will use, but it would take you 70 minutes of lecture time to write it all out in class. Plus, all the time is invested before the lecture, so you can devote all your lecture time to lecturing, instead of writing.
On that note, with slides you can focus on your lecture without being distracted by writing (eg. which part of the board to write the next bit on, how big to write, how to lay it out, whether to erase some parts first). This may sound silly, but for instance my script is beautiful on paper but hideous on a board - every time I must use a board, I always feel very insecure with how ugly and not-neat my writing and drawings look, and this is very distracting to me because it makes the usual public speaking anxiety that much worse.
Generally, the maximum speed you can write legibly at is not guaranteed to be greater than the optimal speed of covering the material. With slides, there is less danger of having to spend a long time writing out lengthy material that can be understood very quickly, but only once all of it is displayed/written. But conversely, if you are lecturing faster than you can write, how will students keep up with their notes?
You only need to prepare slides once, and can reuse them with minor updates. If you tend to write on the blackboard, you will have to write all of the material again and again every time you teach the class (although you can reuse your notes).
You can (and should) speak information which is related, but not identical, to what's on the slides. Often slides have more basic, fundamental points as you develop more complex ideas verbally. In this way, students can easily solve problems like "what does that new term that the lecturer just used mean again?" and follow more easily. You can essentially have 2 parallel threads running simultaneously, and students can switch back and forth between them depending on which one is easier to follow. Imagine you are teaching archeometry to a class that is half chemists and half historians. During the chemistry slides, the chemists can listen to you talking about the intricacies of the chemistry, while the historians focus on the basics from the slides. Then during the history part (eg. metallurgical developments), vice versa. But it can be argued that such heterogeneous teaching is not a good idea in the first place.
The slides can be given out to students for study in their own time. (but so can scanned notes, photos of the board, video recordings of lectures, etc)
If slides are given ahead of time, students can print out slides, and significantly reduce how much writing they need to take by writing down only things which you say that are not on the slides (because they are better explained verbally, or because they came up after a question, etc). The caveat is that writing helps retention, so this may actually impair students' ability to learn the material on the slides.
With slides, you can display arbitrary images. For instance, complex patterns that would take time to draw on a board, plots that are hard to draw just right, photographs (both ordinary and technical such as micrographs), busy figures with many intricate features (sometimes the figure simply cannot be any simpler). But, you can just print handouts with the pictures, or use a good old fashioned slide projector.
You can include things like animations, video and audio. Animations are useless 99% of the time (although they may help at times). Video and audio can be invaluable in some classes, for instance videos of behavioral psychology experiments or audio in a music theory class. But then again, you can still teach your class on a board and only go to slides for the audio/video.
A bright rectangle of light in the middle of a dark room will focus everyone's attention on it. But on the other hand, it also makes it very easy to zone out and catch up on some quality Z time. (plus, if you darken the room it will be hard to write notes)
Conclusion
It is possible to name many advantages of using slides, especially if you don't mind very specific advantages. However, most aren't real advantages, in the sense that you can have a lecture that's as good, and probably better, by:
- Preparing paper notes for yourself.
- Practicing the lecture before class and timing yourself.
- Thinking about your learning objectives for the lecture and being mindful of them to stay on track and not get derailed.
- Preparing handouts if you must show many images that are hard to draw or many equations that take too long to write out.
- Using the computer only to show video clips and so on, and then returning to your usual lecture after the video is over.
If you follow these, there are very few real advantages of slides, and many disadvantages (distraction, restricts your freedom of drawing and writing to PowerPoint's formatting options, not effective for learning). This is, of course, if your goal is to have a very effective lecture.
Sadly, often people aim instead to spend as little time and effort as possible on the lecture. In that case, PowerPoint will produce a mediocre lecture, while writing on the board will produce an awful one. Too often people take the idea that "old fashioned teaching on the board is better than slides" and then think they can do a good job with inadequate preparation by just teaching from the board instead of using slides. They end up rambling on and on, and after the lecture all the students say to each other, "What the hell was he going on about up there? I didn't understand a single thing!" (unless this happens to be an extremely talented teacher)
On the other hand, it is impossible to lecture from slides with zero preparation (since you do have to make the slides at least) so it forces some semblance of coherence on you, although not much. So, if you are going to do your students a disservice by not preparing adequately, you are better off with PowerPoint (but only in the sense that you are better off losing a hand than losing your arm).