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The terminology used to describe Japanese hotel rooms is pretty much the same as that used in Europe and elsewhere.

Best way to demonstrate what
single room
twin room
semi-double room
double room
triple room
typically mean in most modestly priced business/tourist hotels is to see them.

Click on the links above from the Kyoto Garden Hotel.

It's pretty typical for a 'business' hotel in Japan (although the majority of those who stay here are generally tourists).

It's common for semi-double rooms to be offered at two different prices - a lower one for single/one person occupancy and a higher one for double/two person occupancy. You may even see rooms with double beds for two being sold at the same price as two single rooms (for one).
I happen to know that the Grand Takanawa Prince in Shinagawa doesn't have single beds in any of its single rooms - they are all doubles. But this is an exception rather than a rule. (although semi-doubles in single rooms may be more common than I thought - see below)

My husband and I have often stayed in semi-doubles (I'm 40cms wide at the shoulder, MrLapLap is 50cms - but I would not recommended one for a couple with a combined width of more than 90cms).
To be honest, I don't notice that much of a difference between staying in a semi-double to staying in a double bed as a couple, the 18cm difference is pretty negligible as far as I'm concerned.

In addition to the rooms linked to above, there are hotels which offer Queen bedded rooms and King Bedded rooms - usually these hotels are more expensive, but there are exceptions (such as the Comfort Inn chain mentioned by abmj-jr).