The second chapter of Massekhet Megilla continues the discussion of the public reading of Megillat Esther on Purim. The Mishna teaches that the Megilla can be read in any language, as long as it is a language that the people understand. Even someone who does not understand Hebrew can fulfill the mitzva of hearing the Megilla by listening to it being read in Hebrew.
All of this is true with regard to reading the Megilla; how about the Torah itself?
The Gemara discusses whether the Sages felt that, “Kol ha-Torah bi-leshon ha-kodesh ne’emrah – whether the entire Torah is said in Hebrew.” Rashi interprets this line to be a reference to public Torah readings. Tosafot, who are in agreement with Rashi that the discussion is whether public Torah readings must be in Hebrew, ask whether there are any Torah readings that are, in fact, true obligations. Their explanation is that this is a reference to those parts of the Torah that we are obligated to say on specific occasions, e.g. when halitza is done (see 25:5-10), when bringing bikkurim (see 26), etc.
The Rashba brings this suggestion and adds that the Gemara might be referring to the mitzvah of reading Parashat Zakhor, which is a Biblical obligation according to all opinions.
Rabbeinu Hananel is quoted as explaining this discussion as relating to the question of whether the Torah can be written and translated into other languages, an issue that was discussed at some length by the Gemara in the first perek (see daf 3).
There are other opinions (see the Ritva, for example) that suggest that the tradition to have regular public readings of the Torah dates back to the time of Moses, who established this practice. Thus there is some level of obligation in the standard weekly Torah readings.