Type C connectors are reversible and can handle up to 3A at 5V. That's way bigger than the actual 500mA we are restricted to. https://en.wikipedia.org/wiki/USB_Type-C
(USB 3.1 standard have even 20V, 5A specification, but I believe this is only for power applications, not for data. Still need to read the standard.)
USB 3.1 includes USB Power-Delivery 2.
Power-Deliver 2 defines a standard for varying the power supplied over the power supply wire in a USB cable.
The standard defines 5 profiles:
Profile 1: 5V at up to 2A (this is basically what most USB is already)
Profile 2: 5V @ 2A, 12V @ 1.5A
Profile 3: 5V @ 2A, 12V @ 3A
Profile 4: 5V @ 2A, 12V and 20V @ 3A
Profile 5: 5V @ 2A, 12V and 20V @ 5A
There's only one power wire, so only one voltage can be supplied at a time.
Basically, when you plug a PD-compliant USB cable into a PD-compliant power-supplying device, the cable can report to the device which profile it supports (this communication happens over the power supply wire). (To help avoid confusion, PD-compliant cables are REQUIRED to have a PD logo on them.)
And then when you plug a power-consuming device in, the power-supplying device and the power-consuming device can talk over the power wire and decide what the power supply should be, and can vary it on the fly (and actually, which device is supplying and which is consuming can change on the fly, too).
The way the profiles work, and power-supplying device of a given profile can support a power-consuming device of its own profile or lower.
The power wires don't carry any data (other than the power negotiation), but they also don't involve the normal USB data connection at all. You can have a single USB 3.1, PD profile 5 cable supplying 20V@5A and also carrying data at the same time.
Note that all of this is completely separate from the USB Type C connector specification. USB Type C does not have to support USB 3.1 or USB Power-Delivery 2, and USB 3.1 does not have to use USB Type C connectors.
It's going to be really nice when USB 3.1 and USB Type C are widely adopted enough to become the norm.