In order to verify a transaction, you need to know that all of the transactions that came before it were also valid. Suppose Bob gives you some bitcoins. In order to verify that transaction, you need to know that Bob obtained that money from a valid transaction. Let's say he got the money from Alice. Now you need to know where Alice got the money. And so on, all the way back to the miner who first produced the coins. And that's just for one transaction. In order to verify all transactions sent to you, you need to be able to verify every single transaction that has ever taken place in the history of Bitcoin, and this is exactly what the client is doing when it is synchronising with the network. When doing this for the first time, the client has to not only download the entire transaction record (which is currently nearly 4GB in size), but also verify every single transaction. This can take a while. However, once it has synchronised the first time, the client only needs to download and verify transactions that have taken place since then, so it is much faster.
Thank you for this very clear explanation.
But yes, making the process faster is a good idea.
