"I eat breakfast."
を is used to indicate the direct object of a sentence; i.e., the thing the verbs affects, in this case the breakfast (あさごはん) that's being eaten. は defines the topic of a sentence, as in the general thing you're talking about and can often be translated as "regarding" or "as for." If you were to use は instead of を in this sentence, it would mean "the breakfast eats," which is obviously not right.
There is a more formal name for each of the meals as well, however duolingo focuses mainly on the less formal (asagohan, hirugohan and bangohan) . Which all share 'gohan', meaning 'meal', or 'rice'. The more formal names are: choushoku, chuushoku, yuushoku, which all share 'shoku', from 'shokuji', also meaning 'meal'... Confusing huh!
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Honorifics can have several functions and origins, aside from just making something sound more polite;
There are cases where adding an honorific can change or clarify the meaning of a word:
水 - water お水 - clean drinkable water
さけ could refer to 酒 "alcohol" or 鮭 "salmon" but お酒・おさけ is always "alcohol"
はな could be 花 "flower" or 鼻 "nose" but お花・おはな is always "flower"
昼 can refer to both "Noon" and "Daytime" but お昼 with an honorific is specifically "noon" (and 昼間・ひるま is specifically "daytime)
お昼ご飯 is then more specific "noon-rice"; "lunch"
Often they are placed on words of cultural importance.
お風呂 "bath", traditionally done in temples as part of cleansing ceremonies
お茶 "tea" traditionally served in ceremonies
ご飯 "rice" a staple food item, served with every meal and by extension became synonymous with "meal"
お昼 could be used in this way as lunch is traditionally the meal you are most likely to socialize during. It is also the meal more likely to be prepared for you by someone else (it's an honor to receive a packed lunch). In elementary schools as well this is an important time for learning about community and sharing as it is common for the children to take part in serving food to their fellow classmates.
There is also simply word beautification or 美化語・びかご
An honorific お before ひる is easy to say and sounds nice, whereas あさ and ばん do not so much.