Suppose I have a 10 Gbps interface in a router.
Does that mean the maximum amount of traffic I can send through the interface will be some combination of input/output rates up to 10 Gbps, or can I have up to 10 Gbps in each direction (input and output at 10G)?
It depends™. Normally for a 10GBit/s interface it means 10GBit/s full-duplex, meaning you can receive and send at 10GBit/s at the same time. Sometimes marketing gets in the way and you get stuff like "This linecard does 260GBit/s" just to realize (before buying it, hopefully) that they meant 130GBit/s in and 130Gbit/s out. But for a single interface it should always be full-duplex.
That being said the practical maximum speed of the interface will depend on a whole bunch of factors, for example the speed of the backplane, oversubscription of the linecard (and utilisation of the other ports on the linecard), amount of packets (many small packets are much more "expensive" to handle than fewer, bigger packets with the same amount of GBit/s), etc.
If we assume 10G Ethernet which is full duplex, then yes, 10G and 10G out.
