When I built my computer I had a USB 3.0 cord where one side looked like a normal USB to stick into a USB port but the other end has this blue thing:
Where do I stick that in?
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That is a 19 pin USB header connector. The header connector would plug into your motherboard, and then you could add internal USB devices. I have one which I believe is used for a card reader and I think I also had to connect a header to enable a second USB 3.0 port that is built into my case. I'd have to actually look in my case to double check what I used it for.
That is a male USB3 (always colored blue with 19 pins) header cable. I don't know why it would have a male USB connector at the end of it though.. Perhaps it's designed for direct USB access from another host or connecting USB components internally, like a USB port on your case. I suspect OP has misidentified the connector at the end of the cable. It is most likely female because there is very little use for an internal male connector.
Here is an image of what I suspect to be OP's cable actually looks like:
As other answers have said that is a connector for plugging into a USB3 motherboard header.
A cable from that to USB 3.0 plugs makes no sense. I expect you have misidentified what is on the other end of the cable and your cable actually has sockets on the other end. Plugs and sockets can look quite similar if you aren't looking carefully.
If I'm right the purpose of that cable is to allow the motherboards USB3 header to be connected to the front panel ports on older cases. When USB3 was first introduced there was no front panel header for it and cases with front USB3 ports came with regular USB3 plugs intended to be plugged into sockets on the rear panel.
Another possibility is that the picture you posted doesn't actually match the connector you have (I notice it's a picture taken from DX, not a picture of your cable). You may see a cable with USB3 plugs and a male header connector for the opposite problem of connecting a newer case to an old motherboard.