Most traditional Asian martial arts use prearranged solo forms or kata (in Japanese) as a primary training method. There are pros and cons to solo form training, and it's important to understand what they should and shouldn't be used for.
Training with a partner is almost always better than training without one. If you're training for self defense, fighting, or combat, the application of your training will always be against an opponent. Even if you're isolating techniques in the air to work on mechanics, you're better off having a partner in front of you as a target. Additionally, techniques do not exist in isolation. They are always in response to a threat or attack. Therefore, they are better trained in that context...in response to a real threat or as a counter to a real attack.
Solo forms can be a good way to pass on a catalog or group of techniques without the need for writing, pictures, or video, and they can be an effective way to train that comprehensive group when a partner is not available. But they should not be used in place of partner training or when a partner is available, except for the time it takes to learn them.
I hesitate to teach solo forms and generally do not. It's easy enough for a practitioner to drill singular techniques and combinations on their own, or to "shadow box" as if there was an opponent attacking them. If/when I do teach or demonstrate a solo form, it's only so a practitioner can train a series of techniques without a partner, with a particular purpose.
The Fundamental Five form in the video above, for example, is a nice way to drill fundamental default responses when a training partner is not available. I occasionally use it while traveling, to keep the default responses fresh in my mind. I use a couple of others for similar reasons, primarily as an easy way to train repetitions of groups of techniques.
Solo forms can be used, especially in front of a mirror, to work on and improve the mechanics of techniques, structures, and footwork without being inhibited by a partner. And because they're done without a partner, they can be practiced with full speed and power with no chance of injury. (Of course prearranged partner drills can also be done this way!) Therefore, they can be a decent way to compensate for the lack of full intensity training in methods that do not allow for it, if you're alone and do not have pads, bags, or targets to practice on.
Solo forms can be done as moving meditation, to focus or relax the mind, and to relieve stress. While partner training can also do this, some people find it easier to do when alone. However, because self defense and martial arts training does involve application against an opponent, the practitioner should apply the mental clarity and focus experienced in solo forms training to partner training.
If I haven't said it enough, solo forms should not be used when a partner is available. Many traditional martial arts schools use them as the primary method of training, and they're the basis of advancement through the belt system. This is misguided at best, and a conscious way to keep students paying at worst. If you're training with a group of students, surely your time would be better spent perfecting your techniques against a real human being! Save the solo forms for when you're...solo.
- See more on self defense training.