Technically speaking, synchronizing is the process of downloading and verifying all previous Bitcoin transactions on the network. For some Bitcoin clients to calculate the spendable balance of your Bitcoin wallet and make new transactions, it needs to be aware of all previous transactions.
This step can be resource intensive and requires sufficient bandwidth and storage to accommodate the full size of the block chain. For Bitcoin to remain secure, enough people should keep using full node clients because they perform the task of validating and relaying transactions.