The Weekly Halachic Analysis
While you could have thought that there's nothing to lose by answering amen if you didn't hear the bracha, the gemara seems to shatter such an idea. Shockingly, the Gemara Brachot 47a states that if you didn't hear Amen, you should not answer an Amen Yetoma, an Amen, which is orphaned and separated from the bracha. Moreover, Ben Azzai says not only is it forbidden, but if you do it, there is a curse that such a person should pass away, leaving his children orphans, Chas VeShalom! What could have possibly prompted Chazal to consider answering Amen Yetoma such a grievous sin?
In order to address our question, perhaps we can gain some insight from seeing how the Rishonim defined the parameters of Amen Yetoma. Rashi and Tosfot ask that the Gemara Sukkah (51b) seems to contradict the Gemara Brachot. The Gemara Sukkah relates how there was such a multitude of people in the shul of Alexandria that some people couldn't hear the Shaliach Tzibbur. To facilitate people answering Amen, the gemara says, the Shaliach Tzibbur would wave a flag as he finished the bracha so everyone could see that they should answer Amen. Seemingly, this gemara takes for granted that it is permitted to answer Amen even if one didn't hear the bracha. Rashi and Tosfot both answer that answering Amen is only an issue if you don't know which bracha was made or if you don't know if someone made a bracha at all. If you know that someone made a certain bracha, however, even if you didn't hear it, you can say Amen. That's why the people of the shul in Alexandria were able to answer Amen even though they didn't hear the bracha.
Based on the explanation of Rashi, one could suggest that the reason that saying Amen without knowing which bracha was made is so severe is because Amen is meant to be a statement affirming the truth of the blessing, expressing one's faith in Hashem's abilities and praise. If you don't know which bracha was made and you still say that you affirm its validity, your words become meaningless. Moreover, your intended praise of Hashem turns out to be hollow and without understanding. That's why, says the Maharal, unlike a bracha which is valid if said without understanding as it is intrinsically meaningful, however, an Amen is a statement of Emunah which is useless without understanding.
Summary of the Daily Halacha's
- Chazal viewed the recitation of Amen very highly. In fact, Chazal tell us that responding Amen is of greater significance than reciting the Beracha. The failure to recite Amen is considered a gross transgression, while responding Amen with great concentration opens the gates of Gan Eden. 
- The letters of Amen are the root letters of the word Emunah, belief or trust. By responding Amen one declares: "I believe in the bracha that I have just heard and I affirm its truth." Additionally, when responding Amen one should have in mind the beginning of the Bracha, "Baruch Atta Hashem", that Hashem's name is Blessed. 
- One should answer Amen to any blessing one hears whether he wishes to fulfill an obligation or not. Moreover, the obligation to respond Amen even applies to a Bracha that does not contain Hashem's Name, such as answering to a Mi Sheberach or HaRachaman. 
- The proper intention of the word Amen changes with the Bracha. When answering Amen to Birchot HaMitzvah or Birchot HaNehenin, one's intention should be to affirm the truth of the Bracha and his belief in it. When answering to Birchot HaShevach, one should have in mind that he is affirming the truth of that praise. When responding Amen to Tefillot one's Amen should be a request of Hashem to fulfill that prayer. 
- When reciting Kiddush on Friday night, we say the words "ויהי ערב ויהי בקר" quietly before saying "יום הששי". In truth, ויהי ערב is actually the second part of the Passuk which precedes יום הששי. We don’t say those words out loud because the first letters of יום הששי ויכלו השמים form the name of Hashem.
- Rashi (Brachot 47a s.v. Yetoma) and Tosfot (Brachot 47a s.v. Amen)
- Regarding the halacha, whether the opinion of Rashi is accepted, see S"A 124:8
- This explanation of Amen Yetoma is developed by Rabbi Zalman Melamed on yeshiva.org.il. Rav Soloveitchik in Reshimot Shiurim (Brachot 47a, p. 501 s.v. VeNirah) explains that Rashi and Tosfot hold that Amen is a function of expressing one's Emunah in the content of the bracha, in which case only knowledge of the bracha is necessary. The Rabbenu Yonah, however, understood that Amen is a way of accepting the bracha upon oneself, in which case, having knowledge of the bracha without hearing its words isn't sufficient.
- Netivot Olam (Netiv HaAvoda ch. 11; Sifrei Maharal Edition v. 1, p. 112)
- Gemara Brachot 53b, Chaye Adam (Klal 6:1), Gemara Shabbat 119b, Rashi Shabbat 119b s.v. BeChol
- Shulchan Aruch 124:6, Mishna Brurah 124:24
- Shulchan Aruch 124:6, 189:5, 215:9
- Shulchan Aruch 124:6, Mishna Brurah 124:25
- Rama 271:10, Levush 271:10, Aruch HaShulchan 271:25, Chatom Sofer OC 10