If you're wondering what you get with a softphone that you won't with a standard phone handset, then that depends on the service. Business-class softphones offer all kinds of features related to online meeting collaboration, call routing, multi-line conference calling, and more. From a residential VoIP perspective, you'll most often find video conferencing (though more and more this is becoming a separate product from most providers), a voicemail-to-text converter, detailed call records, and user controls for users other than yourself. Some services also offer faxing, text chat, and call metering so you can see how much you're spending.
For larger systems, and for systems where security is critical, the old internet connection is no longer adequate. The internet doesn't do quality of service (QoS), and bandwidth can be unpredictable. Network congestion can ruin a business phone call, and activities such as DNS hijacking can put your business at risk. While we all love the internet, it's not necessarily the safe place for your business voice communications. If you fall into this category, remember that while the internet runs using the IP protocol and VoIP runs over the IP protocol, that doesn't mean that VoIP must run over the internet. You can get the same software benefits of VoIP by running your voice network over dedicated lines. Sure, it will cost more, but it will also ensure crystal clear voice quality as well as the ability to implement much-improved data security.
The caveat there is the proverbial fine print, usually located just below the really attractive dollar figure. This small print generally details exactly how many months that nice number will remain in effect before the bloom comes off the rose and you start getting billed a much higher number that represents the service's actual cost. Many providers don't even print this higher number on their websites, so be sure to ask the sales guy on the phone before you sign up. The nice number that pulled you in can often double or more once the introductory period wears off. Some providers even attach a minimum length of time that you'll need to suffer these higher costs before you can change or modify the service without getting hit with an additional early-termination penalty fee.
The only additional piece of equipment that you need is an Analog Telephone Adapter (also referred to as an ATA) that allows you to connect your existing telephone to your home Internet. This equipment is typically provided on a free lease basis from the home VoIP provider that you choose, or you can use you own device if you prefer. You can also use IP phone(s) instead of using the ATA with your existing analog phones. The sound quality is better but there is more up front cost as IP phones are more expensive than the ATA devices.