I am learning about prayer services and was wondering what is "ya’aleh v’yavo" and when do we insert the “ya’aleh v’yavo” language into our davening?
Yaaleh VeYavo (literally: it should go up and come) are the first unique words of an paragraph inserted into all non-Musaf prayers (ie. Shemoneh Esrei/Amida) as well as the Grace After Meals on biblical Jewish holidays (that is, Rosh HaShana, Yom Kippur, Sukkot (all 7 days), Shemini Atzeret, Pesach (all 7 days), Shavuot, and Rosh Chodesh).
In it, we pray for God to remember us and our merits and bless us on holiday X (roughly speaking). It is important as it is the primary vehicle whereby we mention the holiday in prayers (something we are supposed to do) and its omission usually (and there are specific exceptions) necessitates repeating the prayer in question.