"AMR

Stands for (Audio/Modem Raiser) Which is used to convert analog audio to digital audio the card is said to be raiser because it raises the audio"

Edit: That is incorrect. AMR stands for "Audio/Modem Riser". The AMR slot's purpose was similar to that of the, then standard, ISA slots, but specifically designed to accommodate smaller, inexpensive modem riser cards, audio riser cards and network riser cards. Intel introduced them on September 1998 as a way to reduce the total cost of computer systems by dividing the logic between the riser cards and their respective controllers on the motherboards.

Later, Intel replaced AMR slots with CNR (communication and networking riser) slots. Though the two are similar, they slightly differ structurally and CNR cards also differed in two other areas: CNR supported Plug & Play cards and they offered the option to be either software based (via the CPU) or controlled by hardware acceleration (dedicated ASIC). To my knowledge though, riser cards that work in AMR slots also work in CNR slots. Neither slot gained popular acceptance by users, either initially or in time. This was likely because the riser cards relied on the CPU to handle alot of their workload, noticably slowing it down. So that's probably why you won't find AMR-compatible cards anywhere today. In 2000, ACR (Advanced Communications Riser) slots replaced both AMR and CNR, but ultimately integrated components made all three slots obselete.

Sources:

Wikipedia.org

Andrews, Jean. A+ Guide to Managing and Maintaining Your PC, 7th edition.

Boston, MA: Cengage Learning, 2010. Print.

Note:

Nothing is "raised" (as suggested earlier by another user). The reason AMR slots accommodated audio cards is likely because it was it was a low priority component (in terms of the bus traffic going to the south bridge and CPU). Regardless of this, analog to digital audio conversions occur on integrated circuits on the sound card and doesn't raise the volume or any other aspect of the audio data (or data on modem/network cards for that matter).