[ In this context, earth-like means a terrestrial planet (ie made of metal and rock as opposed to a gas giant), having a mass comparable to earth, and orbiting its star at a distance such that its temperature is consistent with the presence of liquid water (liquid water may not actually be present, the temperature just can’t be so cold that water would freeze nor so hot that it would boil). That leaves a lot of possible differences between this planet and earth. ]
Since proxima centari is a red dwarf it is probably tidally locked. Unless you are talking about a large moon of a gas giant, or a dual planet system like the earth-moon system.
It could be tidally locked and have life, but it would be an “eyeball” planet
http://www.space.com/20856-alien-planets-eyeball-earths.html
Earth like should not be taken to mean habitable. Odds are that the planet they found is not habitable. The temperature I referred to would be the temperature calculated based on the irradiance of the star and the orbital distance of the planet. To be earth like means that the average planetary temperature must be 32-212F. That would be the case for a tidally locked planet, but the average temperature would not reflect actual conditions. The day side would be much hotter than the average with the night side much colder.