When people say speed they usually mean bandwidth (i.e., the amount of data you can send or receive in one second). This is generally expressed in terms of bits per second (bps) and more typically as Kbps, Mbps or Gbps referring to Kilobits, Megabits or Gigabits per second respectively.
Having a bandwidth capacity that is able to support your particular Internet usage is very important. However, this minimum speed requirement is usually lower than most people think. For example, Netflix recommends only 25 Mbps for their highest 4K video and only 5 Mbps for regular HD video. For a group video call of 7+ people, Skype recommends 8 Mbps and only 1.5 Mbps for a single HD video call. And as for online gaming, actual gameplay tends to be very efficient with most games needing less than 10 Mbps. For many applications (VoIP, video conferencing, gaming) a low delay and low delay variation can be much more valuable than just having additional bandwidth.
The bottom line is that although having a higher speed connection certainly doesn't hurt, having a high quality (and highly reliable) connection is usually worth much more. This is similar to how most people are not as concerned about their car's top speed as they are about it always starting and not requiring frequent repairs. In the end, a lower bandwidth connection that runs clean almost always produces a better user experience than a higher bandwidth connection that has loss, timeouts and retransmissions. The testing that monitor-io specializes in is designed around these exact realities.