A cordless phone consists of a wireless handset that communicates to the base station by radio waves. The base station plugs into a standard telephone line jack and uses ac adapter to power the phone.

Many cordless phones offer additional handsets that will 'talk' to the base unit and can be placed in any room where no telephone jack exists.

Sound Quality
You will want to use a corded phone to get the best sound quality possible. However, If you want the convenience of cordless phones, you may notice a reduction in sound quality.

Wikipedia explains it this way:

"Plain old telephone service" (POTS) landlines are designed to transfer audio with a quality that is just enough for the parties to understand each other. Typical bandwidth is 3.6 kHz; only a fraction of the frequencies that humans can hear, but enough to make the voice intelligible. No phone can improve on this quality, as it is a limitation of the phone system itself. Higher-quality phones can transfer this signal to the handset with less interference over a greater range, however.

Most cordless telephones, though, no matter what frequency band or transmission method is used, will hardly ever exactly match the sound quality of a high-quality wired telephone attached to a good telephone line.
This constraint is caused by a number of issues, including the following:
1. Sidetone: hearing one's own voice echoed in the receiver speaker
2. A noticeable amount of constant background noise (This is not interference from outside sources, but noise within the cordless telephone system.)
3. Frequency response not being the full frequency response available in a wired landline telephone"

Why the Phone Frequency May Matter To You
 
900 MHz Phones
There are a few analog amplified cordless phones still operating on the 900 MHz frequency. Many people with hearing aids have had good success with these phones.
It is an old frequency and not used as often. It has a lower operating distance than the other frequencies.
(Some phone models include HC-A55, CL-C425P, CL-C435)

2.4 GHz Phones
Many amplified cordless phones operate on the 2.4 GHz frequency.

There are interference issues with the 2.4 GHz phones because many other electronics now use this frequency. You will likely suffer interference if you use a use a wireless router for your computer. Bluetooth devices, microwave ovens and baby monitors can all cause interference as well. 

You might be able to change the channel on the wireless router to reduce interference. The interference you'll notice is a static sound that degrades sound quality while on the phone. 
(some phones models include: KM-KCS50i, HC-PHONE3, CL-C4105, CL-C4205, CL-C4210)

5.8 GHz Phones
Phones that use 5.8GHz digital transmission offer less interference with other electronics and should perform better than a 2.4GHz phone. However, there is an even better transmission available now. (DECT 6.0)
(some phone models include: CL-C4220, CL-C4230)

DECT 6.0 Phones
The best choice for a cordless phone is a DECT phone. It offers the longest operating range and least change of interference because it operates on a radio frequency that is licensed for the exclusive use of cordless phones.

A DECT phone operates on the 1.9GHz range, but you'll see it advertised as DECT or DECT 6.0. 
(some phone models include: Most all Clarity, Serene Innovations and Clearounds phones; CL-D613, HC-A300)

Hearing Aid Compatible

Hearing Aid Compatibility simply means that a phone creates a magnetic signal as well as the audible sound signal. The magnetic signal is used by hearing aid telecoils that enable a person to use the phone by turning off their hearing aid microphone and pick up the magnetic signal through the hearing aid telecoil.

There is no standard for the strength of that magnetic signal. That is why a phone that is hearing aid compatible doesn't necessarily provide a strong enough magnetic signal to be useful for the hearing aid telecoil.

You can use an inline phone amplifier to increase the signal strength or you can purchase an amplified telephone to create a better signal.

Hearing Aid Telecoil

Sometimes people who wear hearing aids will notice a loud squeal when trying to place the handset next to the hearing aid. This squeal is caused by the hearing aid microphone. A telecoil is an option on hearing aids that eliminates the squeal when using the phone because the hearing aid microphone is bypassed.

The telecoil is designed to pick up the magnetic signal created by a hearing aid compatible telephone. The hearing aid telecoil converts the signal back into an audible signal. This eliminates the squeal created by the microphone. Most telecoils are turned on by pushing a button or flipping a switch on the hearing aid.

Some hearing aids have 'automatic telecoils' that will automatically turn on when they sense a magnetic signal.

TIA-1083 Compliant Cordless Phones

A cordless phone labeled with TIA-1083 Compliance means that hearing aid users will experience significantly reduced problems with audio interference during conversations. This is a relatively new standard that was adopted and implemented in record time in the telecommunications industry.

How it came about: When digital cordless phones came on the market, hearing aid users began experiencing interference when trying to use the phones. Studies were conducted which resulted in the creation of the new testing protocol. More information can be found in this flyer.