A partition on a hard disk device is a unique segment that is separate from other segments on the device.
A primary partition - also called a boot partition - contains a tiny code to find operating system boot loader, and passes the control to boot loader which starts booting the operating system. In most versions of Microsoft Windows operating systems, the first partition (drive C:) must be a "primary partition".
A common partition type code for a primary partition used with Microsoft Windows NT 4.x, Windows 2000, XP, Vista, Windows 7,8 & 10, Windows 2003, 2008 & 2012 Servers is NTFS.
The number of partitions you can create on a hard disk or a USB device depends on the device's partition style. In Windows, the MBR (Master Boot Record) describes how a disk is partitioned, which partition contains the boot sector and where the boot sector is located.
On MBR devices, you can create up to four primary partitions, or you can create up to three primary partitions and one extended partition. You may create only one extended partition on a drive device. Within the extended partition, you can create an unlimited number of logical drives.
You can add more space to an existing primary partition by extending it into adjacent, contiguous unallocated space on the same disk. To extend a partition, it must be formatted with the NTFS file system. You can extend a logical drive within contiguous free space in the extended partition that contains it.
If you extend a logical drive beyond the free space available in the extended partition, the extended partition grows to contain the logical drive as long as the extended partition is followed by contiguous unallocated space.
Another partitioning scheme is GPT, which overcomes some MBR restrictions. The GUID Partition Table, known as the GPT, is a popular disk partitioning scheme used across most operating systems, including Windows and Unix-class operating systems such as Mac OS X. It was introduced by Intel in the late 1990's and has since become the standard layout of the partition table on a physical hard disk. It is a successor to many partition tables, such as MBR and APM, overcoming their limitations of using 32 bits for logical block addresses and a standard block size of 512 bytes.
You can read about how everything looks on a low level, and what physical partition damage and recovery process looks like in Partition Recovery Concepts.