Irish doesn't use use Subject-Verb-Object as English does. It uses VSO. So if you see a sentence "Tá sí beag", while directly translating to something like "Is she small", it means "She is small.". Other examples include "Tá tú óg" (You are young) and "Tá sé mór" (he/it is big).
tá is a verb. The subject of tá is the object of the verb "have" in English.
Irish, in common with languages like Russian, Korean and Hindi, among others, doesn't have a verb that means "have". Irish uses the phrasal verb tá ag for this purpose, and uses the preposition ag to indicate the possessor (the subject in English). Pronouns combine with prepositions, so aige indicates "he has", aici indicates she has, ag Pól indicates "Paul has".