I think it's a pretty vague phrase and its exact meaning variesfrom on context to another.
Basically, I think it means to live causing as little further harm to the environment as possible. Some of the things we do to the planet cannot be “sustained indefinitely”: either the resources needed will eventually be exhausted (such as fossil fuels) or the damage caused to ecosystems, the environment and the planet will be too great to allow us to continue (such as the results of continued activities causing global warming).
In the UK there is concern for the damage caused by the production, use and disposal of plastic. Not using plastic where it could be avoided could be said to contribute to “living sustainably”. It is impossible to continue indefinitely using landfill sites to dispose of the increasing amount of refuse. Producing as little waste as possible, reusing it or recycling it would contribute to “living sustainably”.
Organic farming, self-sufficiency, composting toilets, solar, tidal and wind power are further examples.