Between is a place neither here nor there. It is where the Dragons travel when they teleport from one place to another. It is a kind of hyperspace. To go between places takes a minimum 8 seconds, no matter the distance. It is, however, also possible to go between times ("timing it"). The time it takes to go between times is proportional to the length of time travelled. 450 Turns appears to be near the limit for a healthy young adult, judging from Lessa's near-fatal Jump.
The phrase "to go between", when used without a stated destination, refers to a dragon suiciding, by going between and staying there.