logic gates: current driving capability
In that context, 'large driving capacity' means sufficient output current to drive typical loads at something approaching the full speed of that logic family's gates.

Examples of typical loads are:

(1) A number of input stages of the same/similar logic family. The maximum number of loads ('fan-out') depends upon the logic family but generally improves with newer families. Guide numbers are only 5..10 loads for early families up to 1000's for later families (refer to family specs' for specifics). A further limit is the capacitance of an increasingly large number of longer interconnecting tracks with stubs at each gate, which will reduce signal speed and/or raw signal quality.

(2) Parallel buses of control and data signals with timing related o each other (e.g. memory bus, multi-board interface bus). Again, larger/longer interconnecting tracks will increasingly reduce signal speed and/or raw quality.

(3) Line driver/buffer circuits. For outputs at different signalling standards (e.g. communications, displays) or controlling higher-power loads (e.g. solenoids, motors, lights).

There's plenty more that could be written on the subject but this illustrates the point for your further reading.