A floppy disk drive consists of a spindle motor attached to a mechanism that grabs the center of a disk and rotates it at certain speed which is measured in RPM, or rotations per minute. A digitally shaped analog signal called a "flux" is either "played" or "recorded" onto a magnetic floppy disk using a read/write head. The head is attached to another motor called a "stepper" that allows it to move along the surface of the disk into 40-80 fixed positions. On most drives, the motor rotates at 300 RPM for "double density" or 360 RPM for "high density" drives. The head detects these changes in the magnetic flux of the disk as it spins, amplifies them, and sends then to an attached controller board. The controller board refines this signal into digital data that is sent to the host computer. Disk drive sizes are most commonly 8", 5.25", or 3.5", although some other odd sizes exist.
A floppy disk consists of a mylar-coated magnetic surface that is rated to store a certain number of flux reversals (from positive to negative, or negative to positive) within a defined area of the surface at a certain speed, at a certain TPI (tracks per inch, which is how close they can be to each other), at a certain coercivity (which is how strong the signal is). 5.25" and 8" disks are in a soft plastic shell that is stored in a sleeve for protection, while 3.5" disks come in a hard plastic shell for durability. Despite the hard shell, 3.5" disks are still considered "floppy". Drives can be either "double sided" meaning the can use the front and back of the disk at the same time, or "single sided" meaning only one side is used. Since most disks are double-sided, you can typically flip the disk over and use the other side on single-sided drives. Double density and high-density disks have different coercivity levels and cannot be interchanged, or the data will not be able to be written properly.
Because of the need for proper clocking, data is encoded so that it cannot violate the rules. The different encoding types include GCR (Apple, Commodore), FM (Atari 8-bit, many other early systems), or MFM (Amiga, Atari ST, PC, many others). These encoding rules, whether implemented in firmware or software, dictate that the data is written in a way that it can be read back exactly the same each time.
The concentric circles on the disk that the flux reversals are recorded on are called tracks. The stepper motor can move and stop at different tracks on a disk, typically around 40 in total for single/double density, and 80 for high density.
In most 40-track systems, the head is too wide to write to just one track at a time, so even though the drive can step to those tracks, every other track may be skipped by the firmware. The common terminology for the step in between each track in this case is a "half track" and a specific track would be referred to as (for example) "35.5" instead of the actual track (which would be 71).
On most disk systems, tracks are further divided into sectors, which are sections of each track typically divided by "sync" marks. A sync mark is a special pattern on the disk that tells the controller where the data starts. Different drives store data at different "bit densities" (essentially clock speed rates of the read/write hardware). However, most systems are locked to a specific density on all tracks.