Nagasu means flow or current (like a stream).
Practically Nagasu has ‘simply’ 2 meanings or ways to use. One is to parry the attack, the other is to let the attack pass your body.
In the second movement of Kihon Gumite Yonhonme for example, you connect your hand to the opponents attack and then ‘weight’ your Shuto to pull the opponent into the direction of your Nagashi Uke. It means to parry.
Nagasu is also known as to let the attack pass your body. Easily said, when you are ‘not there’ the attack passes the body. However, that could be either to escape or to avoid. For karate, avoiding (Kawasu) is more proper as this means that you are within Maai to hit the opponent instantly. It is better to be hit slightly than to step to the outside.
Stay close to the opponent.
Nagasu comes with body movenent, it can't exist without it...
...Remember Ten I, Ten Tai and Ten Gi?
Ten I and Ten Tai together are what makes Ten Gi "Nagasu". In plain English that means that moving your body and twisting your body are what allows you to avoid the attack. What dictates the logic movement of your arms.
Then Ten Gi comes in.
The following techniques are all applications of Nagasu because you:
There is a difference between Kihon and Kumite. One key is to not keep the punch in the extended position. In that sense, Nagashizuki from Ido Kihon is already an application. When dealing with an opponent, it's necessary to understand how you can apply basics and connect one technique to the other.