Demonstrativa: este, esse und aquele

English points with two words, "this" and "that". Portuguese has three, and the extra one is anchored to the person you are talking to: "this here by me", "that there by you", "that over there, away from us both".

Este livro aqui é meu. - This book (here, with me) is mine. Essa camiseta é nova? - Is that T-shirt (the one you're wearing) new? Aquela montanha é o Pão de Açúcar. - That mountain (over there) is Sugarloaf.

The adverbs follow the same three steps: aqui (here), aí (there, by you), ali / lá (over there).

The neuter forms

Isto, isso, aquilo point at something without naming it, like "this thing" or "that": O que é isso? - "What's that?" Isso! on its own means "Exactly!" They never stand before a noun: "this book" is este livro, not *isto livro.

How Brazilians really use them

In everyday Brazilian speech the line between este and esse has largely disappeared: most people say esse for "this" as well, and isso for both isto and isso, adding aqui or aí when the distance matters: esse livro aqui. Careful writing and European Portuguese keep the three-way system.

Fused with prepositions

Demonstratives fuse with de, em and a: de + este = deste, em + esse = nesse, em + aquela = naquela, a + aquele = àquele, de + aquilo = daquilo. Moro nesta rua. Gosto daquele restaurante. Writing them apart (*de este) is an error.

Time

For time, este is the period you are in or the next one (este mês - this month, esta semana), esse often refers back to something just mentioned (nesse dia - on that day), and aquele is the distant past (naquele tempo - in those days). In Brazil esse mês for "this month" is common in speech.