A small electronic circuit, used with wire antennas for shortwave listening. If receiving signals below 30 MHz is your goal with a random wire, then yes, you will benefit. Connect to receiver input on one end with a SMA Male - SMA Male pigtail, connect to random wire on other side with spring-loaded terminals - that's it.
Requires no power, connect-and-forget, spring-loaded terminals hold wires securely.
Balun in the name means balanced (two wires, one in each hole) to unbalanced (coax cable). Technically, a 9:1 UnUn (Unbalanced to Unbalanced) is the appropriate tool to use with a single wire.
In real life, even with just one random wire, adding a Balun One Nine results in more signal on HF, and if you connect two equal length random wires to both hole, an even better signal.
Draw your own conclusions.
Should you buy one?
Only if you want to get the best performance from a length of wire on frequencies below 30 MHz.
Desperate for HF reception but cash-strapped? Spend $10 on a Balun One Nine and download Oliver Jowett's HF drivers (download link) for SDR#; a usable combo, play and have fun until you save up enough for an upconverter.