Ping relates to responsiveness not overall speed.
On a basic level ping would be how long it takes for water to get from the beginning of a house pipe to the end of it (and technically back again).
It tells you how quickly a drop of water would get from one side to the other, but it doesn't really tell you how much water can get there. That's where bandwidth or "speed" as you put it comes into the equation.
1MB DSL, 4MB DSL, 10MB DSL will all take equally long to get a single drop of water from one end to the other as the latency (ping) is inherent to the technology. However the different line speeds can get considerably more water there as it becomes faster.
So for latency intensive requirements such as online gaming or voice calls the ping/latency is more important than the overall speed. For streaming video on the other hand the overall speed/bandwidth is what makes you receive higher quality video and the latency/ping is somewhat irrelevant and only really helps it start faster.