Ordinal numbers are adjectives used to organize persons and things into a sequence or order. Since they are adjectives, they agree in number and gender with the nouns they modify.
Primero and tercero drop the -o in the masculine singular adjective form.
el primer día
el tercer año
In Spanish, the ordinal forms are used most commonly for the numbers 10 and under. They are seldom used after the tenth.
Ordinal numbers indicate the order in which something occurs (first, second, third, etc).
"Cardinal numbers" are regular numbers—one, two, three, etc.
When you get to eleventh you can say the cardinal numbers and they mean the same thing—el once (the eleventh). There are other ordinal numbers that continue after ten, but they are not as common as one through ten. The ordinal numbers primero and tercero drop the "o" before a masculine singular noun. For example, el primer chico; el tercer libro.