Not related to this service but for VPN in general, it does this by preventing your ISP from throttling specific sets of your traffic. If they know you're downloading a torrent, they'll lower the speed. They don't know what you're doing via VPN because it's all encrypted. For an example, Verizon would limit Netflix streams at SD rate but if you watch Netflix via VPN, you would see SuperHD or 1080 rates because Verizon doesn't know what you're doing via VPN.
Of course, if you're using an ISP that doesn't throttle and follows network neutrality properly, than VPN won't increase the speed for you.
Netflix buys backbone access from a backbone provider, the ISPs then have a connection with that backbone providers. The pipe from that provider to the ISP gets congested and there is an argument as to who should pay.
However the pipe to your VPN data centre and Netflix's backbone provider are congestion free so you get a faster rate.
Internet routing isn't as dynamic as we imagine and whilst Netflix offer to put caching boxes in the ISP network, the ISP's are not keen on that solution.
End result you are performing a manual re-routing of data to bypass congested links.
Compression is one simple answer. Another is that any server in a datacenter is going to have much better routing and connectivity than a residential connection. If you have good (uncongested) routing to one VPN server, you can use it as alternative to your ISP's network.
Some gamers use OpenVPN, with encryption and compression disabled, which functions as a very low latency UDP tunnel.
Home -> Good ISP routing -> VPN server -> Game server (20ms RTT)
Right, but the traffic still passes through your residential connection, so you're still limited to the bandwidth provided by your ISP; if anything, the overhead of VPN will decrease internet speeds there.
In other words, a VPN isn't an alternative to an ISP's network, but rather an additional system on top of it.
On the other hand, a VPN will generally bypass an ISP's own DNS servers, which could afford some speedup when performing domain name resolution/lookup if the ISP's nameservers are sluggish (though configuring your system to use alternate nameservers would do this without the overhead of a VPN).
If your ISP provides only a congested route to say, Netflix or YouTube, then a tunnel through a better connected VPN server can allow you bypass that route entirely, increasing throughput and lowering latency.
In the case where an ISP provides optimal routing, it cannot improve latency. Compression and buffering, among other things, still may offer better throughput.
True. In that case, though, the better advertising approach would be to state that directly rather than vaguely (and inaccurately) claiming a "20x" boost in download speed.
Of course, if you're using an ISP that doesn't throttle and follows network neutrality properly, than VPN won't increase the speed for you.