The term "cylinder" is a holdover from the old days when you had one head for each surface. Back then, the logical organization really could be visualized as cylindrical. Partitions were horizontal slices of cylinders. Nowadays, of course, you have multiple heads for each platter, so there isn't anything truly cylindrical about it anymore.
The underlying concept, however, is still valid. Although the multiple read/write heads can function independently, they are all still attached to a common arm and move together, even though they may be positioned over disparate logical partitions.
When reading data, each head reads a portion of the "cylinder" in sequence. Then the heads are moved to the next physical location. Seeking is the most expensive operation a drive can perform, so the fewer the number of seeks the faster you get the data. The larger the partition, the more heads are involved in reading data before the next seek, and the more data you can move before physically re-positioning the head assembly.
Hope that makes sense. Believe it or not, I once taught the subject to field engineers! But it's been a long time since the days when I sat on a computer room floor with a dismantled washing-machine sized 300MB CDC drive.