The snapshot is done to save the size of the growing database.
It saves all the balance while removing the history and data of all the tx and start fresh from there again where all addresses with balance acting like new genesis address and no further history or data attached.
individuals can keep their old data base to load up for checking old transaction histories but not use in the new snapshot, this is a basic model of snapshotting the network, there are more efficient ways in the making.
so after snapshots you will not find any transaction histories or at times the balance (if you had done any transactions before on the seed) in your seed anymore and because of the way security is handled on your wallet client to protect the entrophy of each address's "private key" after its used, and because they way seeds connects to its corresponding addresses in a certain order(address a-z), you will require to "generate addresses" until your local database finds the latest address which had your balance in prior to the snapshot.(if your balance is at address c, then you will need to generate 3addresses to reach to address c and see its corresponding balance.)
now to explain why sometimes we need to do "claiming"
there is few different claiming periods that has happened in iota.
the first one is to claim your genesis balance from the ico.
then there are periods of claiming to a new design of iota's internal workings that will not be compatible with old seed/addresses (you can think of it as a hardfork to get your head around it).
In the future as long as there is no big internal design changes, we do not expect the need to do any more claim processes. But you'd never know, iota is still a beta technology and may need major design changes to fit what the future has to tackle, so best is to keep yourself informed from time to time, iota will always give a fair amount of time for claim periods if there is any need to a change.