In this case "To" replaces the expression made of demonstrative pronoun "to" [this] and the verb "jest" [is]. The demonstrative pronoun "tamto" does not have such an ability, and in fact, "tamto" written alone is weird in Polish, in this sentence it requires for example an additional "to" ;-) - "Tamto, to duży pająk"
The special word "to"
"To" is a special word, or rather 5 words that have the same spelling.
1) One of the most important pronouns. They very often replace that, what in English is written this, it or even the (as Polish does not have articles). "To" is used for the nouns that have either neutral or unknown gender (while asking "what is this?" about an unknown object); there is also form "ta" for feminine nouns and "ten" for masculine.
2) A particle, that replaces verb "być" (to be) in complex predicate: "Pies to zwierzę" (Dog is an animal); "Warszawa to stolica Polski" (Warsaw is the capital of Poland) , "Ania to dobra uczennica" (Ania is a good student) , "Czas to pieniądz" (Time is money); This particle may also replace a contruction "to jest" (this is, it is): This is the case here: "To ja" (This is me), "Kto to?" (who is this?), "To prawda" (This is true), "To tu" (It is here), "To za daleko" (It is too far away), "To duży pająk!" (This is a big spider!)
Attention 1: "To to jabłko, o którym mówimy" (This is the apple that we are talking about) - here are 2x "to": case 1 and case 2, side by side!
Attention 2: With "to", you have to use the noun in nominative case: "Pies to zwierzę"; "Warszawa to stolica Polski"; "Ania to dobra uczennica". With "jest" you have to use the noun in instrumental case: "Pies jest zwierzęciem"; "Warszawa jest stolicą Polski"; "Ania jest dobrą uczennicą". This thread can also be interesting: "To jest kaczka"
3) A connective that joins two sentences, of which the second is the consequence of the first: "Zdejmij koszulę, to ci przyszyję guzik" (Take off the shirt, then I'll sew the button), "Przyjechał wcześnie, to dużo załatwił" (He came early, so he arranged a lot). It may also connect sentences in a dialogue: "Kupiłem chleb. -- To dobrze." (I bought bread. -- Good.); "Przestępczość wzrasta. -- To źle" (The crime rate is rising. -- Too bad"); "Pewnie on ukradł konia! -- To, to, to, to!" (It was probably him to steal the horse! -- Yes, yes, yes, yes!);
Attention: In this sample dialogue: "Źle wyglądasz. Are you sick? -- To nie to. Mój kot dziś zdechł." (You look bad. Are you sick? -- No, it's not that. My cat died today.) - there are 2x "to": case 3 and case 1. The phrase "To nie to" or "Nie, to nie to" is a very popular expression serving as an introduction to explanation of negative answer.
4) A particle serving for greater expression: "Któż to przyszedł?" (Who came!?); "A to się wszyscy zdziwią!" (Oh, everybody will be surprised!)
5) A particle serving in a sentence as a sort of interlude, for example to separate the known (or obvious information) from something new, or to put more stress on that: "W zeszłym roku o tej porze, to lało" (Last year in this season, it was heavily raining); "Tę książkę, to pamiętaj mi oddać" (That book, well, remember to give it back to me).
This may be also interesting to read: "to" (in Polish)