For the unbelievers, here's the definition:
Definition - What does Spin-Up mean? Spin-up is when a disk in a disk
drive speeds up to the required revolutions per minute for effective
writing to or reading from the disk. Conventional hard disk drives
have one or more platters that revolve mechanically on a spindle while
reading and writing elements alter the magnetic surface of the disk.
A hard disk drive (HDD), hard disk, hard drive, or fixed disk[b] is an electro-mechanical data storage device that uses magnetic storage to store and retrieve digital information using one or more rigid rapidly rotating disks [SPINNING] (platters) coated with magnetic material. The platters are paired with magnetic heads, usually arranged on a moving actuator arm, which read and write data to the platter surfaces.2 Data is accessed in a random-access manner, meaning that individual blocks of data can be stored or retrieved in any order and not only sequentially. HDDs are a type of non-volatile storage, retaining stored data even when powered off.3
Introduced by IBM in 1956, HDDs were the dominant secondary storage device for general-purpose computers beginning in the early 1960s. HDDs maintained this position into the modern era of servers and personal computers.
hard disk drive and spinning (rotating)
And finally, in this day and age:
in British English from the Collins Dictionary
(tr, adverb) computing
to create (a virtual machine) using a cloud-computing service
to spin up a new server
spin up a server