First, I would like to beg forgiveness for the somewhat confusing and possibly inaccurate node title. The "mind/body problem" part is fairly non-controversial, although it is probably not the language that Spinoza would have used himself. And I don't know if "solution to" would be the right term, but it comes closer than "views of", "position on" or other such term. I would also like to offer an obvious caveat that this is a simplified explanation, and more intense scholars of Spinoza could probably add or subtract much from my explanation. With those caveats out of the way---
Spinoza believed in an all-encompassing God, with infinite attributes. Humans are only aware of two of those attributes: mind and body. For those not familiar with scholastic terminology, mind and body were traditionally viewed as substances in themselves. For Spinoza, God was the only substance, and things that seemed to be substances were only attributes. Understanding the scholastic background also puts the terms in prospective: while Spinoza was a great believer in God, his pantheistic notion of God was classified as atheism by many.
Because mind and body were just separate attributes of a single substance, they were not causally linked. Mental events didn't create physical events, or vice-versa. All events were just the one substance behaving in a perfect, predetermined manner, as manifested by two attributes of that substance. Without agreeing with Spinoza's views, I have to say that his view of physical and mental processes was extremely sophisticated, and seems to be beyond the reach of many who are trying to figure out the matter today.
To illustrate the acausal nature of body and mind, I will use the example of a triangle, an example that Spinoza would have liked, since he was even more besotted with geometry than most philosophers. Physical and mental processes are analogous to the sides and angles of a triangle. Take, for example, an equilateral triangle with three 60 degree angles, and sides of one unit each. Now, if we increase one side of the triangle, the angles have to change. But this is an atemporal relation. In our ideal triangle, it is not as if the increasing side increases in size, and then taps the shoulders of the angles and tells them they have to change. Although the lines and the angles seem separate, they are actually just attributes of the one triangle.
So in Spinoza's view, the physical substances of our brain did not somehow tap the shoulders of our emotions and tell them to change, which they were then obliged to do. There is no mental homunculus that is responding to physical events, either with free will or in a predetermined way. There is not a molecule of octopamine that is bumping our minds into feeling angry. What there is a molecule of octopamine bumping into a receptor, and this is just a complimentary attribute to our feeling of anger. The two events are like the lines and angles of a triangle: seemingly different, but determined by the overall shape of the phenomena.
From a philosophical viewpoint, this is I feel a very good explanation, very elegant, very sophisticated, especially considering the time it was developed. I feel that there would be two major objections to it. The first is that from an existentialist or phenomenological viewpoint, Spinoza's perfect rationalism doesn't totally explain the actual way that consciousness, subjectivity, or emotions are actually experienced. There are many existentialist critiques of perfect rationalism, but Spinoza, living some two centuries before even the protoexistentialists, can hardly be blamed for not taking them into account. The second objection is that while Spinoza (as many people today) believed that every single mental state could be composed of several simpler mental states, and that this composition could be directly traced to a physical state of the brain composed of smaller brain states; this was not something that Spinoza could ever actually test. That is, while he had a good philosophical theory, it also attempted to be a scientific theory, unsuccessfully. But again, since he was a rationalist, and was living long before any type of real neuroscience, he can hardly be blamed for this. However, people who still espouse Spinoza's view (although usually not knowing it is his, or understanding the sophistication of it) in the current day must make a better explanation for how the philosophic theory accords with scientific evidence.