"Rail-to-rail" is a marketing term used to describe an op amp whose dynamic range is able to reach the extremes of the supply voltage. This can refer to either the output or both the input and output.
It is not possible for the output to exceed the positive or negative supply voltage (which is why these are commonly referred to in US-English as "supply rails"). This is one of the key differences between the ideal op amp model and the real article.
As a counterexample, the ancient LM741 op amp is not "rail to rail", and here's why: in the datasheet Electrical Characteristics table, the Output Voltage Swing is rated +/-16V under the test condition of supply voltage=+/-20V. So the output can only get within about 4V of the supply rails. (There is some dependency on the output load resistance.) This is the key specification you can check on the Electrical Characteristics table pertinent to rail-to-rail output.
This limited dynamic range is very problematic at lower supply voltages. Attempting to operate the LM741 from +/-5V supplies, leaves only about +/-1V of dynamic range for the output. And operating LM741 from a single +5V supply leaves no dynamic range at all: the output is generally stuck in the middle and LM741 is not usable at such a low supply voltage.
It's also possible for some op-amps to accept inputs that are at or even beyond the rails -- Maxim Integrated makes a line of op amps marketed as "beyond the rails" (for input).