What is the reason why one may not eat prior to hearing havdala on motsei shabbos??
A possible reason comes from the Gemara in Pesachim 105a where doing so is dangerous.
דרב הונא חזייה לההוא גברא דשתה מיא קודם הבדלה אמר ליה לא מיסתפי מר מאסכרה דתנא משמיה דרבי עקיבא כל הטועם כלום קודם שיבדיל מיתתו באסכרה רבנן דבי רב אשי לא קפדי אמיא
Rav Huna saw a certain person who was drinking water before Havdalah and said to him "Are you not afraid of choking?". For it is taught in the name of Rabbi Akiva: anyone who tastes anything before he makes Havdalah, his death will come about by choking. The Rabbis of the study hall of Rav Ashi were not concerned about water
Hope this is helpful.
When I was writing the answer, @RoshHaYeshiveh already answered.
I want just to add to his answer a couple of details and express a certain disagreement. In most situations, eating is prohibited before Havdala. But if he was eating (e.g.Seuda Shelishit which began before sundown), he can continue to eat, despite the end of Sabbath and even to drink (e.g. if he was eating peanuts and drinking wine), he can continue to drink coffee. But if he was drinking some beverage before sundown and continue until night, he need to stop the drinking. there is an opinion following which all the above is right only at a time which is not clearly night, but if there is clearly night, even in middle of meal, he need to cover the bread and to bless Havdala on a cup before the end of the meal. RMA said that the first opinion is most spread.
Shulchan Aruch Orach Chayim 299, 1:
אסור לאכול שום דבר או אפילו לשתות יין או שאר משקין חוץ ממים משתחשך עד שיבדיל
אבל אם היה יושב ואוכל מבעוד יום וחשכה לו אין צריך להפסיק (אפילו משתיה) (בית יוסף).
ואם היה יושב ושותה וחשכה לו צריך להפסיק:
ויש אומרים דהני מילי בספק חשיכה אבל בודאי חשיכה אפילו היה יושב ואוכל פורס מפה ומבדיל וגומר סעודתו:
הגה: והמנהג פשוט כסברא הראשונה
The source of the above Halachot is the snippet of Gemara immediately above the text cited by @RoshHaYeshiveh:
Said R'Amram to them, thus did Rab say: It makes [it an] appointed [meal] in respect of kiddush, but it does not make [it an] appointed [meal] in respect of habdalah.
But that is only in respect of interrupting [the meal], viz. , that we do not interrupt [it]; we may not however commence [one]. ; And even about interrupting we said this with respect to eating only, but not with respect to drinking.
And with respect to drinking too we said this only of wine and beer: but as for water, it does not matter.
Now he differs from R'Huna.
Rav Huna reported in name of Rabbi Akiva that to taste anything before havdala can lead to diphtheria. I am not sure that it is the reason, the reason is apparently in the words of Rav Amram (Tur and Bet Yosef stated as Rav Amram, against Rav Huna probably because of Rsv Ashi who is the latest Amora and disagreed with Rav Huna concerning water):
לקידוש - קובעת, ולא להבדלה קובעת. והני מילי - לענין מיפסק, דלא מפסקינן. אבל אתחולי - לא מתחלינן.
Shabbat is a caesura between before and after. We are in duty to feel this concerning meals. Lifetime is delimited by Shabbat. There are halachic translation:
Shabbat fixed a prohibition to eat before Kiddush. Shabbat does also fix at its end a prohibition regarding eating before Havdala. This last point concerns only prohibition of beginning activities, but not prohibition to continue already started eating. Therefore to continue an already started drinking of beer (but not water) is prohibited.
If there is no wine, see SA 396:
אם אין לו יין ולא שכר ושאר משקין יש אומרים שמותר לו לאכול ויש אומרים שאם מצפה שיהיה לו למחר לא יאכל עד למחר :
Some poskim who stated that he can eat and some else stated that if he will get wine tomorrow he cannot eat until the havdala of tomorrow.
There are 2 Havdalas on shabbat. One in the davening, and one on a cup. There are 2 aspects to shabbat - shomor (keep) and zachor (remember). In short shomor means do not do the 39 forbidden acts, and zachor means do the positive commandments - drink wine, eat bread - oneg or physical pleasure of shabbat etc.
The 1st havdala in davening is just before the 1st time we ask for something post shabbat. We dont ask for our own personal needs on shabbat, which is shomor. After the 1st havdala we can break this.
But the second havdala is for zachor - we can only get physical pleasure from the week after this havdala. So we drink after the havdala. Thus we should not eat before this havdala - as this havdala makes the separation between our shabbat physical pleasures and our weekday physical pleasures.
I am not providing sources, and if you do not like this answer, I am sure there will be plenty others with sources to choose from.
The Mishnah Berurah (271 and 299) explains that the prohibition on eating and drinking before kiddush and havdallah are because the obligation to make kiddush has already fallen on the individual to be performed immediately and not delayed.
The Magen Avraham in S.A. 271(see also how R' Akiva Eiger explains the Magen Avraham there) explains that the prohibition of not eating before lulav or other mitzvos is not like kiddush (or havdallah). By mitzvos like lulav, a person may not eat a meal before fulfilling the mitzvah, but may snack. This is because the sages did not want us to forget the mitzvah entirely while the day will just go by. The mitzvah did not fall on the person at sunrise to be obligatory immediately at sunrise. However, kiddush and havdallah are to be fulfilled the moment they arrive. Therefore, they should be performed right away and we may not eat anything, so as not to push them off at all. (according to many poskim, kiddush by day (as opposed to Friday night kiddush), does not have this restriction until the normal daytime mealtime arrives after davening).