"It is necessary to empty the bag."
Translation:Il faut vider le sac.
'il' would mean a fairly specific thing required the action whereas 'on' is a more impersonal one/someone/anyone. This English sentence is framed in a similarly general manner. There is no actual it making a request here. So while 'on' is not usually a word for word translation of 'it' it's use here is far closer in spirit to the meaning of the English sentence taken as a whole.
In summary it is that peculiar English usage of 'it' when there is nothing really there to be an 'it' that is fooling you, not so much your French! :)
The back translation would be: "this is necessary to empty the bag", which has another meaning (this thing is necessary in order to empty the bag).
What makes "c'est nécessaire de vider le sac" improper is the fact that if you ask the question "what is necessary?", you end up with 2 subjects for the same verb: "c" is necessary and "vider le sac" is necessary. This is why it is not a correct construction, even though the French use it massively in speech (and in informal writing).
Remember that c' is a real subject and that impersonal phrases (matching English impersonal phrases with "it") need "il".
In the learning process it is somewhat disheartening when one comes across the constant switching of meaning that is attached to an apparently innocuous little word like 'il'. On it's own it means 'he' or 'it'. 'faut' means 'must' (forget about 'doit' for a moment). However, when 'il' and 'faut' are put together they do not mean 'he must' or 'it must', they mean 'It is necessary', and if one adds 'savoir' to the sentence it suddenly becomes, 'you need to know', and if you then replace 'savoir' with 'faire attention' it now becomes 'be careful'. I can't quit now. Not after all I've put into it, but this aspect of french sure makes me want to.
"faut" does not mean "must" but "is necessary" or "is required". It is defective, which means that it can only show in an impersonal construction with "il" which will never mean"he".
Any sentence having "il faut" will need an interpretation because there is no equivalent in English. So you have to get used to the various ways it can be adapted, because "il faut" is the 14th most frequent French verb.
C'est en effet une formulation qu'on entend beaucoup, mais qui est grammaticalement incorrecte.
Le pronom impersonnel de la langue française est "il": il est nécessaire de... ou il est nécessaire que...
"C'est" a un sujet réel: "ce/c'" signifie "ceci" ou "cette chose" et en tant que pronom démonstratif, il ne doit pas servir à construire des formules impersonnelles.
De même qu'on ne dit pas "ceci est nécessaire de vider le sac", ou "cette chose est nécessaire de vider le sac", vous ne devez donc pas employer "c'est" dans cette phrase.