Since FSN can be sliced into time slices it can get a little confusing how much FSN you actually have. When you slice a full FSN (by full FSN I mean FSN without any type of TL and that you could send to exchanges or use in liquidity contracts) it will be divided in two parts. One which lasts from current time, until a time you chose to slice it at, if that time is 4 months into the future you will have created some 4 month TL FSN and simultaneously sent the slice off to another wallet (as the slicing happens in a tx). The second part remains in your wallet and is the infinity end of that FSN. The infinity end can also be sent other places, if desired (but, like all TL FSN will not be accepted by exchanges). As long as you have the infinity end of FSN, you can be considered its true owner.
Normally, you just keep the infinity end in the original wallet until the time has passed for it to become full again (in our example this would be 4 months), but it's entirely possible to do other things with it, such as 1. Try to trade it on the quantum swap market. 2. Make this FSN full early, if you can either retain the original slice, or if you find another slice that fills the gap between current time and the missing time.
In order to make full FSN out of such a combination of slices, you must use a wallet that supports the "send back to assets" function. Currently this can be done with either whallet.net or myfusionwallet.com. The option to use this function only appears if you have all the necessary time slices in your address, thus it can't be attempted unless it's all there.
A big point of confusion is that send back to assets is also necessary to perform on single infinity ends who have already reached the point where they last from current time until infinity. It's a common misconception that these will automatically return to their state as full FSN. But it is not so, and thus every time you want any type of TL FSN to again be full you must piece it/them together with the send back to assets function, even if it's already just one piece. The reason for this is that the blockchain will need to perform a TL-related tx to recognize that this change of state is happening.
In MyFusionWallet the option to send back to assets is represented by a wallet icon next to the relavent asset. As seen in the image TLs can be used in all ways not just for FSN but for all Fusion assets, in this case we have the option to make a one-token asset called IPIR full again.
In whallet the send back to assets function is reached by first 1. selecting Time-locked Assets, then 2. choosing Send for the asset that can be made full. On the next screen fill in the amount and 3. pick the "to Assets" option and then 4. hit Send.
In November 2022 a hardfork of Fusion launched which to an extent removed the need to "send back to assets" for FSN (this has simplified things for stakers and other users of TL FSN. Specifically time-limited FSN sent to exchanges long ago could finally be cleared in exchange wallets). But the concept still remains in full for other Fusion assets, and is also useful to be aware of for anyone trying to piece together their TLs.
So what is infinity balance? With balance of FSN being divided into full FSN, regular time slices and infinity end slices (time limited). It can be quite confusing to realize just how much FSN you have. Therefore the simplest way to recognize "true balance" of FSN is to consider how much FSN you would have at the infinity of time (assuming nothing changes). This amount is what best represents your true, real balance of FSN and is used by block explorers such as FSNEX to organize all fusion addresses in "rich lists".