The basic answer is this:
"Tu" is the second person, equivalent to the singular "you" in english.
"Você" is a formal way of addressing someone and it came from the expression "vossa mercê", which means "your mercy". So, it makes sense to use the third person when using "você". Like if you were conjugating "ele" ("he") ou "ela" ("she").
The (slightly) more complicated use of the two words is this:
In Portugal, the rule is to use "tu" when you want to be informal. "Você" is used in a formal and more polite situation. Some people find it kind of rude to use the actual word "você". So, to be even more polite, you would use the name of the person and conjugate it as "você". So, if you're asking a woman called Maria if she wants somehing, you could do it in the following ways, from casual to formal:
"(Tu) queres alguma coisa?", the word "tu" is optional, because the verb already states that we're using the second person.
"(Você) quer alguma coisa?", "você" is also optional, for the same reason.
"A Maria quer alguma coisa?", you use the third person in the verb conjugation and state the person's name.
In Brasil, it's much more common to use "você" for everybody in any situation. There are some exceptions. For example, in Rio de Janeiro people use "tu", but conjugate it as the third person, so you get things like "tu é", which for me is not correct portuguese, but it's used in spoken language anyway in some regions.
As for the plural, it's normal to use "vocês" both in Portugal and Brasil. And conjugate it as the third person in the plural.
Oficially, the plural form of "you" is "vós", conjugated in the second person in the plural. But this is usually considered archaic. You can see it in some films when the action happens in medieval times, for example. But as usual, there are exceptions. In northern Portugal, it's still quite common to use "vós" and it's completely correct.