Earlier quoted context omitted.
You always give a transaction you received before in order to spend coins. However, you're supposed to use a fresh (source) address for every new transaction (the wallet software does it for you). You can't (with the default wallet software) chose which transaction (called unspent transaction) you use in order to spend you coin (this is called coin control). That is, you can trace coins, not owners, unless you're alw…
If you say, get paid in Bitcoin, one transaction a month, and that's the only way you earn Bitcoin. Will you use the same source address all month?
You can invent a new destination address each time you transact (to get paid or to receive change). You make a new address by picking a random number and doing some math.