What does this mean? You may help me, by explaining those points in a different way.
Sure.In Bitcoin you have to either trust others for knowing your balance or downloading the block chain and seeing it by yourself. If you be a Bitcoin node, which is the second option that is to verify the entire chain, you'll be sure that every information you receive is true and if it's not you can reject it. You're independent of any other nodes' words. Your computer checks the validity of each block and it sums your final balance given your address. Thus, you're following the chain with the most work which is whole system's reliance and you know that anything you see is valid.
On the other hand, if you need other nodes to know your balance you're automatically dependent to their words. For example, your address may have 1 BTC, but a malicious node may return you that you have 0 BTC. There is no way to verify that this is true, you have to trust it.
The best way for maximizing your security and privacy is running a pruned node which doesn't require to keep the whole chain. Yes, you have to download it all and verify each block, but after an amount of blocks downloaded you get rid of the previous blocks and thus, you don't need hundreds of gigabytes to operate.
You may have spotted the following common used phrase: “Don't trust, verify!”. That is why.
