I decided to speak about Loshon HaKodesh this past week. Thanks for all the suggestions from everyone and especially to Chaim Brown (aka the Divrei Chaim) for suggesting this topic.
Why is it called Loshon HaKodesh
There are 3 opinions why the language is called loshon hakodesh.
The Rambam in Moreh Nevuchim (2:8) writes that it is called loshon hakodesh because there are no words in this language that describe the reproductive organs of a person.
The Ramban in Shemos (30:23) argues on the Rambam. HE says according to teh Rambam it should be called loshon nekiah or loshon taharah. Rather it is called loshon hakodesh because this language is used for devarim that are kodosh. HKBH created the world with this language, the Torah was given with this language, nevuah was said in this language and malachim speak this language.
On a deeper level the Shelah writes that all the letters of loshon hakodesh have an effect in shamayim. The letters and the words which these letters make up form the essence of each object and it is an expression of what that object represents in shamayim. For example, a table is called a shulchan. The word shulchan is not just an arbitrary word, but rather the letters "shin", "lamed", "ches" and "nun" (and in that order) represent the spirtual force that makes up a table. This is why the language is called loshon hakodesh.
This idea of the Shelah is found in many sifrei machshava. This is also the explanation given to explain what it means that Adam named all the animals. Adam knew the essence and spiritual makeup of each animal and consequently he gave them the hebrew letters that correspond to them.
Mitzvah to learn loshon hakodesh
Is there a mitzvah to learn loshon hakodesh? There is a Sifri in Eikev on the possuk "v'dibarta bam" that one is obligated to teach his child loshon hakodesh and torah. The Torah Temima writes that from here we see there is a mitzva to learn loshon hakodesh and he expresses astonishment that it is not counted as one of the mitzvos nor is it brought in Shulchan Aruch.He references a sefer he wrote on the topic called "Sefah L'Ne'amanim" which I actually found here The Torah Temima brings a few rayos to his idea. One raya is from the Rambam on Avos 2:1 The mishna says one should be careful to fullfill a mitzva kala like a mitzva chamura. The Rambam says a mitzva kala is learning loshon hakodesh.
Although noone says it is a mitzva to learn loshon hakodesh, Rav Moshe in Even Ezer 3:35 does say that it is a mitzvah to speak loshon hakodesh. However, Rav Moshe also says there is no issur to speak other languages as we see many gedolim spoke other languages.
The Chavas Yair (Siman 120) also writes it is important to learn the laws of dikduk but one should not spend an inordinate amount of time on it.
Although the language is called loshon hakodesh, it is clear from the Shulchan Aruch and poskim that the language itself has no inherent kedusha. The Tashbetz and the Sh'ailas Ya'avetz both poin to out that the Shulchan Aruch (85:2) says you can speak loshon hakodesh in the bathroom. From here we see that unlike a sefer torah, there is nothing inherently kodosh about the language. The MG"A does write that the Sefer Chassidim says one should be makpid not to speak loshon hakodesh in the bathroom. The Chasam Sofer (notes to Shulchan Aruch Siman 85) says that there was an old minhag not to teach small children loshon hakodesh so they won't come to speak it in the bathroom.
Loshon Hakodesh in Halacha
One other are of halach that loshon hakodesh is discussed is in Siman 307:16, The Rema writes that even though certain books are not allowed to be read on Shabbos, if they are written in loshon hakodesh it is muttar since one can learn fromn the language. This is similar to the hetter to read a Get on Shabbos since one can learn Hilchos Gittin from it. The Taz and MG"A disagree with this Rema and the Mishna Berura is machmir.