Translation:Your sister is supporting these people.
Support refers to assistance that is rendered over a period of time, wheras help is mostly meant as one single event.
While they are of course very close here, I'm not sure that we should treat "help" and "support" as synonyms.
I tried "Your sister supports this people", which is wrong (would that be "naród" rather than "ludzie"?). I was corrected to "Your sister supports the people." Why can "tych" be "the" here?
Yeah, 'this people' would be rather strange here and if anything, it'd translate to 'naród', I guess.
Well, very often when you use "the" in English, in fact the meaning is very close to "this"/"these". "the people" would be some specific people, so it would feel better to say "tych ludzi" than just "ludzi" (all people?) in Polish. Generally, we try to always accept 'the' for 'ten' and its forms.