This linguistic terminology generally has caused a lot of miscommunication and misunderstanding.
The notion of not self is that is there no:
- unchanging everlasting component which we can identify as self. Other contemporary teachers tried to identify such a part which they called Atman
- there is nothing to which any one can have absolute or ever lasting control over either externally or internally
Also the notion of self, self consciousness, ego, thoughts relating to oneself all is:
- a source of misery
Since you do not have any control over any of the what make up this self you cannot have futuristes view of your self and destiny. Also since your influence to the external world is limited, you can get to own or control is also limited. But when we think about I will to this or that, there is a sense of absolute control of destiny or the environment. This is delusional as you cannot to things to absolute certainty and any deviation result is you becoming disappointed.
If you drill down more deeply when some tough or contact comes through your sense doors. (E.g. some one is scolding you or you remeber someone is scolding you.) 1st you recognise this is some one is scolding, then you identify this incident it is me who is getting scolded. At this point you get a bad feeling (literally) in your body. You have a mental reaction to this and then form volitional though like I will scold him back. Likewise if it praise you get an opposite feeling. Though this itself is subtle you lose the balance of your mind, as you might get puffed up, when some one does this type of talk. Also you cannot get the pleasantness of praise to last always which sometimes lead to subtle disappointments. Thus each time you get any notion of I, me, mine, etc. coming up in your mind some disappointment is bound to happen if you analyze it fully and realistically, thus not understanding this fast is a delusion. So the notion of no self, in this this context. If you you hold onto a notion of self (Pudgala - Sanna) misery arises, letting go of the notion of self your mind gets free from misery. Hence the linguistic rendering of no self.
Also the absence of anything upon which you can exert absolute control or any component which is permanent, to which you can reliably apply the label this is me or myself - the eternal me (this part of me never changes) or this is image of me (a good person, strong person, etc.) or belongs to me or in my control (this should be as I wish or will it to be) - viz. noting identifiable as self, me, mine, I. Since there is nothing we can use the word or label with the word self, considering either of the properties of everlasting, absolute control, we say there is no self.
This does not mean you do not exist in any colloquial sense or any sense outside the above definitions (permanent, controllable properties). So if you or any body practices to get you mind to be stress and disappointment free, the benefits are to be reaped by the person getting enlightened. So you should be be motivated to achieve it. So do not get some play on words deter you. (These are very difficult to understand concepts, thus should be careful of misconceptions using the same wording or rendering.)
Also developing this notion (any concept or notion is Manasikara) as a beginner (though you have to abandon this view also at higher stages of meditation) can help dissolve your ego, self consciousness, self awareness, concept of self in you mind. This can be an early stage catalyst in your progress (also helping you reduce stress and disappointment due to the concept of I, me, mine) than somethings reducing your motivation to practice
In Buddhism you should experience the peace within this lifetime and in each step you take. More you practice more powerful your peace becomes. Lesser mental reaction you have towards great, pleasant, unpleasant, hurt, sour, etc. feelings caused by external stimuli more balance your mind will be and more peaceful you will get.
Also remember Buddhist concepts are not easily explainable in words as the concepts are not really mainstream, thus the the language and ability to communicate them has not developed. When translating these into languages with not Buddhist or related culture, things are even more difficult.