Meaning of "estar"

Question

¿Estas invitaciones son tuyas?

Here I guess estas means "these" and son means "are".

In another sentence:

Mis libros están aquí.

están represents "are".

I'm a little bit confused. How can I determine what estar means?

Answer 1

1. ¿Estas invitaciones son tuyas?
   Your guess is right: these is the plural demonstrative pronoun and son is one of the forms of the verb to be in Spanish — The other one is están (second/third person plural form).
   Don't confuse estas and estás, the second one is a to be form and then the following sentence would be non-sense:

   ¿Estás vacaciones son tuyas? But
   ¿Estás de vacaciones? (= Are you on holidays?)

2. Mis libros están aquí.
   Words stressed and ending in n, s or a vowel need the graphic accent. Written like,

   Mis libros estan aquí

   makes it readable but incorrectly spelt.

3. be forms in Spanish are two: ser & estar. Study their conjugations so that you don't get confused with the demonstrative pronoun este/esta/estos/estas.
   está/esté/estás/estés are conjugated be forms for estar.

Answer 2

In the first case you are using a pronoun, estas is the plural of esta, which means these and this each one.

There is also a word you are missing that is ésta and éstas, which is also this and that, but when there is no noun. So for example you can say

Me gustan estas manzanas. I like these apples

Which has the noun manzanas, apples, but you could also say

Me gustan esas manzanas, pero éstas me gustan más. I like those apples but I like these more

The pronunciation for those cases is the same, in the first syllable.

Now, estar means always to be (in the first case you had estas/éstas which is something different).

The conjunction is as follows:

Estoy (I'm)

Estás (you're)

Está (this is, it is)

and so on.

I believe the use of estar is pretty clear as it means to be.

Now you also have son in your examples, which indeed means (they) are, but it's a different verb. In this case is the verb ser, which also means to be.

Now for your question to how determine if it's about the verb to be or the pronoun these, among other similar words (este, esté, etc), the easiest thing is to learn the conjugations of the verb. In most cases you can also determine it from the context. They are never written in the same way, and the pronunciation is also different, so that's what you have to out attention on.