In everyday life we take the meaning of infinity to be anything which we perceive in endless amount like space, energy etc. However the meaning of infinity according to our scriptures is a bit different and in strict terms even space is not infinite according to shruti. In chandogya upanishad infinity is described in following words by venerable sage sanatakumara ji. The questioner is narad muni ji. "The infinite is bliss. There is no bliss in anything finite. Only the Infinite is bliss. One must desire to understand the Infinite." "Venerable Sir, I desire to understand the Infinite." (chandogya upanishad VII-xxiii-1) "Where one sees nothing else, hears nothing else, understands nothing else—that is the Infinite. Where one sees something else, hears something else, understands something else—that is the finite. The Infinite is immortal, the finite mortal." (chandogya upanishad VII-xxiv-1) so the great sage sanatakumara ji clearly tells infinity is something where everything is same, everything is part-less, this verse actually also tells us that even panchbhutas are not infinite and they disappear once duality disappears. For exampe space cannot be called as infinite, because in space are scattered millions of galaxies and stars, so it is not a infinite entity. Only brahm is infinite.
Infinity means something "without end". Infinity goes on forever, so sometimes space, numbers, and other things are said to be 'infinite'.
I feel there's a need to make a clarification on the original post. The following are excerpts from some messages given by Shri Datta Swami at universal-spirituality.org. These excerpts are relevant the original post. Do read them when you have the time. 'The infinity of the Universe stands for the existence of unimaginable entity beyond the Universe existing from the boundary of Universe. Unless you accept the unimaginable region beyond the boundary of Universe, you cannot speak of the end of imaginable boundary of the Universe.' 'The word infinity cannot be real unimaginability. An infinite item can be imaginable and can be perceived. For example, the universe is infinite but is perceived. Infinity cannot bring unimaginability. Therefore, there is no use in calling infinite bliss as the characteristic of God. Infinity cannot make the bliss unimaginable and therefore infinite bliss cannot be the unimaginable God. Infinite bliss can only be a characteristic that is associated with God constantly and thus, can be assumed as His real characteristic although really it is not His actual characteristic. Similarly, Jnanam [knowledge] is a special development of Chit. The material of Jnanam is only Chit. The Jnanam may be exceptionally special and can be infinite, but it is still only an item of creation since Jnanam is Chit and Chit is only a special work form of energy.' 'The aim is only to say that beyond the boundary of cosmos, the unimaginable domain exists. In the absence of the unimaginable domain, you have to extend the cosmos to be infinite, which cannot be done since it is a composite of finite parts. Any item that has birth cannot be infinite in the absolute sense. The cosmos is generated by God. The process of generation is also unimaginable since there is no second example to study regarding the generation of imaginable from unimaginable. Generation of cosmos from God is unique example and hence, not only God, but also, His action of process of creation is unimaginable. In the case of unimaginable single God, the definition of infinite is not applicable in a physical sense. Everywhere God is unimaginable and hence homogeneous in the sense that the unimaginable nature is uniform everywhere in God. God has no space in Him, being beyond space from whom it is generated and therefore, God has no internal difference of parts in composite having spatial dimensions, which is called as internal difference (svagatabheda). For the same reason, God has no external difference from another similar God (Sajaatiyabheda). For the same reason, God also has no external difference from other dissimilar items like world (Vijaatiyabheda). All these aspects are explained based on single point i.e., the unimaginable nature due to absence of space in unimaginable God. Based on this unimaginable aspect only, God becomes the material and instrumental cause (Abhinna nimitta upaadaana kaaranam) of cosmos like a magician creating objects in space through an unknowable (temporarily) talent comparable to unknowable (permanently) talent of God. We have no other way since there is no second unknowable permanent talent in the cosmos. One has to accept the finite cosmos or space and one has to also accept the existence of some unknowable item beyond the boundaries of cosmos. If you do not accept such existence, the danger of infinite cosmos (being composite of finite parts) attacks you. For this reason, we say that the unimaginable item exists beyond cosmos, which makes the cosmos finite. The unimaginable nature of God is also proved often by the exhibition of unimaginable miracles by God through incarnations and devotees, provided you have an open mind to study them without bias and prejudice unlike an atheist. Since the way of entry of unimaginable God in to cosmos exhibiting unimaginable miracles is also unimaginable, you cannot object that how the unimaginable domain, which is beyond the boundary of cosmos, can enter the imaginable cosmos. The huge water of the ocean makes a separate boundary from the soil and the same water also exists on the soil (earth) as lakes and rivers. Hence, we do not insist on the infinite nature of God, which means that God must have infinite spatial dimensions. Since God is beyond space, the finite and infinite natures fail in His case. Two similar golden blocks indicate Sajaatiyabheda. Two dissimilar blocks of gold and iron indicate Vijaatiyabheda. The difference between the limbs (quantitatively like two hands or qualitatively and quantitatively like hand and eye) indicates Svagatabheda.'