The definite article ('the') is used because we are talking about the specific communities that the company has worked with, as opposed to all the other communities throughout the world in which it may not do anything. However, in this particular case, it does not really matter if 'the' is used or not, as the communities are further defined within the sentence; so both sentences would be acceptable.
If the specific communities had been defined previously to this sentence, the writer could have said:
xxx company's enduring commitment to these communities reflects its belief in corporate citizenship.
In this case 'these' would be used as a determiner instead of 'the' to refer back to the previously defined communities.
The writer could not have said:
xxx company's enduring commitment to communities reflects its belief in corporate citizenship.
In this case, the absence of a determiner before 'communities' is misleading, as it could lead someone to infer that the company helps communities other than those where it operates.
Finally, you used the verb 'reflect' in both sentences. This verb should be 'reflects', as it is the 'company's enduring commitment' which 'reflect[s] its belief in corporate citizenship'. The noun phrase 'company's enduring commitment' is in the third person singular and so must the verb that follows it.