Wireless communication over short distances
Bluetooth is named after Harald Bluetooth, who was known for his diplomatic skills to get different parties to communicate and trade together in real life. The name is a symbol of the Bluetooth technology's purpose - namely, a communication standard across platforms and products.
Basically Bluetooth technology allows endless possibilities for wireless communication and data exchange over short distances.
More and more widely used in consumer electronics
For ordinary mortals, especially in consumer electronics and gadgets the Bluetooth technology has become widely popular. Now a days most computers, smartphones and tablets / iPad etc. has built-in Bluetooth support, and in this way they can interact to all other types of electronics and gadgets, which also feature Bluetooth compatibility.
For example, Wireless Bluetooth Speakers have become very popular in recent years. Typically, neither smartphones / iPhone, tablets / iPads and PCs have very good built-in sound, so with a Bluetooth speaker, one can easily upgrade the sound quality on the go. As more and more people start using music streaming services like Spotify, WiMP, Deezer, Rdio etc. with their mobile devices, a bluetooth loudspeaker suddenly become a quite popular partner. If the BT speaker is of good quality and based on the latest Bluetooth 4.x standard, they can even be fast enough for movie audio sync - even when streaming from Netflix, NBO, Viaplay etc.
Also within wireless keyboards and mice products, Bluetooth has become quite popular. As more and more consumer electronics and gadgets get Bluetooth keyboard and mouse support, it suddenly makes sense to connect a mini keyboard multiple platforms like HTPC, Smartphones / iPhone, Tablets / iPad, Xbox, Playstation and even newer SmartTVs.
New Bluetooth versions
The Bluetooth standard is like everything else in constant development. The latest version is called Bluetooth V4.x, and it is especially related to bandwidth (how much data can be transferred), speed (how fast it can be transferred), security and energy savings improvements are being made.
So for Bluetooth Speakers, where the need for high bandwidth, high speed and low power consumption is needed in order to transmit music in the highest possible sound quality, while maintaining s long battery life, then yes! - a Bluetooth 4.0 speaker would be the best option. However, that itself is not necessarily a guarantee to get the best sounding speaker, but thats a completely different story ;-)
If we look at wireless bluetooth keyboard / mouse products, we do not have the same huge need for high bandwidth and speed, as input / key entries are not very data intensive. So mostly you see these type of products in Bluetooth V2.0 or V3.0 versions - mainly to keep the price down. Bluetooth V3.0 however provides a bit better performance and power consumption vs price ratio in keyboard/mouse products today compared to Bluetooth V1.0 V2.0.
If you see Bluetooth products advertised with no reference to Bluetooth Version number, you can probably expect it to be based on the fairly outdated thus cheaper Bluetooth 2.0 standard.
Talking together across platforms and versions
One of the reasons Bluetooth has become so popular within short range wireless communication, is that devices can talk to each other across platforms - Whether it's an iPhone, Android device, Playstation, Xbox, PC, bluetooth speaker, bluetooth keyboard / mouse , Headset etc. - Basically, both the host and client just need to have Bluetooth support.
A Bluetooth 4.0 device is even backward compatible and can therefore also be connected to a Bluetooth 2.0 / 3.0 device and vice versa, but nothing is stronger than its weakest link of course. So even if you connect a Bluetooth 2.0 host to the best Bluetooth 4.0 speaker on the market, the sound quality will still be limited to the quality/bandwidth the Bluetooth 2.0 protocol can transfer (due to much lower bandwidth in BT2.0/BT3.0, the music will be significantly more compressed compared to BT 4.0).