One of the ways that Russian orthography differs from English is in its use of capital and lowercase letters. The phrases «прописная буква» and «заглавная буква» mean ‘capital letter,’ and «строчная буква» means ‘lowercase letter.’

Notice that in Russian we say that a word is written "from" a capital letter (с + genitive) not "with" a capital letter.

Rules for Russian capitalization (all in Russian) are available here. One of the curious things to note is that during the Soviet period the names of holidays associated with the revolution were written with a capital letter on the first word (not the others, if any), thus: Первое мая May First, Международный женский день International Women's Day, Новый год New Year's, Девятое января January Ninth. (Why the heck they thought New Year's was a revolutionary holiday is beyond me.) Religious holidays, in keeping with the Communist Party's general denigration of religion, were supposed to be written with a lowercase letter: рождество Christmas, троицын день Trinity Day (which is usually called Pentecost in the West), святки Yuletide. That bit is changing nowadays, and the first letter of the first word of religious holidays is often capitalized. The Soviet period rules are still reflected in some places, including the link just given.

Last but not least, first names, patronymics, Western middle names, and surnames (last names) are always capitalized:

Picky detail: the «II» of Obama's name is said «второй» out loud.