They are certainly handy. You connect an antenna, dial up a frequency on the analyser and you will get an indication of how it presents as a load, including its resistance and reactance. Better analysers have a display to show everything in graphical form. You can buy or build them.
The cheaper analysers have had somewhat mixed reviews so it seems to be a matter of getting what you pay for. The more practically inclined may be able to save by building one. DDS VFO modules and cheap microcontrollers, specifically the Arduino, have revolutionised their construction. Here's some ideas that could be handy:
* AB1ZO homebrew antenna analyser
* Cheap antenna analyser by Electronics Lab
* No frills antenna analyser (video)
* YD1CHS poor man's antenna analyser
* Tenna Dipper another poor man's antenna analyser
PS: Want some practical antenna ideas? Consider this selection of antenna books. They are affiliate links meaning that I receive a small commission (at no extra cost to you) if you decide to purchase.