Keiko aikido is what we do when we are in the dojo. It encompasses the techniques we practise and also includes the way in which we practise i.e. katai keiko, building a strong base by training in a strong and focused manner. Focusing on the correct use of hanmi, hitomi and kenkagoshi, as well as skilfully using awase to break your partners balance. Keiko aikido is incredibly deep, and has a lot of detail that must be studied carefully. You cannot cut corners when doing Keiko aikido. If you do the technique will not work. Keiko aikido is a form of misogi (cleansing) that seek to remove imperfections from your spirit.
Then there is Embu Aikido. This is the style of aikido you use when you are demonstrating aikido to the public. It is softer and more dance like the uke is also part of the demonstration making the attacks appear strong while also taking big clean ukemi ( break falls ) to make the techniques appear exciting and graceful.
The main difference between the two is the substance, Embu aikido is a show , tori and uke work in collaboration to create something that is aesthetically pleasing and interesting to watch. In many cases techniques are modified to allow uke to take big graceful ukemi and attacks while they may look strong have little resistance behind them. Embu aikido papers over small mistakes and imperfections in the pursuit of a form that is pleasing to the eye.
Keiko aikido is the complete opposite. While Embu aikido looks to conceal mistakes. Keiko aikido looks to find problems and expose them. In keiko we collaborate to a point i.e. we don't go out of our way to spoil the technique. But beyond that the responsibility is on tori to take uke's balance and throw him. Keiko aikido is also a secret and should not be indiscriminately shown to the public.
This is not to say that Embu aikido is completely useless, in fact Saito sensei has often said that you should train diligently when you are preparing for a Embu as this will help raise the level of your in general aikido. He once compared training for a demonstration to training for a test.
Because Iwama aikido focuses on strong katai keiko style of training, the more flowing graceful side is often neglected. By taking the opportunity to train diligently for Embus we can study a kind of movement that we usually don't have a chance to practise during keiko. Thereby making our aikido more rounded and polished. As long as our demonstrations don't turn into circus acts i.e. using kiai to knock people over or performing ikkyo with one finger, Embu aikido does have a positive benefit on our training.