INT 13h AH=03h is the mirror of INT 13h AH=02h: the same registers, but the data goes from ES:BX to the disk. It writes raw sectors with no idea what they contain. DOS is not asked and not told: its file allocation table, directories and buffers stay as they were, even if the sector just overwritten held part of them.

That makes it the tool of disk copiers, formatters, boot-sector installers and disk editors, and the classic way to destroy a disk by accident. Overwriting sector 1 of a hard disk replaces the partition table, after which no partition can be found; writing over a FAT or a directory loses files.

The example below is not runnable on purpose: these examples run on a real DOSBox-X, and writing sectors is exactly what they must never do. On the workbench's mounted folder it would only fail (CF = 1, AH = FFh, since there is no disk behind drive C), but with a disk image mounted it would really write. The snippet reads the boot sector of the floppy in A:, changes nothing, and writes it back to the same place, which is the safe shape of a sector edit:

Not runnable: writing sectors could damage a mounted disk image. Try it, if at all, on a copy of a floppy image mounted as A:.
PUSH    CS
POP     ES
MOV     BX, OFFSET SECT1  ; ES:BX = 512 bytes
MOV     AX, 0201h         ; read cylinder 0, head 0, sector 1...
MOV     CX, 0001h
MOV     DX, 0000h         ; ...of drive 00h, the floppy in A:
INT     13h
JC      FAIL1
; ... here a disk editor would change bytes in SECT1 ...
MOV     AX, 0301h         ; write the sector back, same address
MOV     CX, 0001h
MOV     DX, 0000h
INT     13h               ; CF = 1, AH = 03h if write protected
JC      FAIL1

Pitfalls

Status 03h means the disk is write protected, the only error a user can fix. After writing behind DOS's back, DOS may still hold the old contents in its buffers and later write them over yours; disk tools flush with INT 21h AH=0Dh before and after. The same 64 KB DMA boundary rule as for reading applies. Many antivirus programs and some BIOSes watch this function and warn when the boot sector or partition table is written, because that is what boot-sector viruses did.