"Tapping into" appears to be derived from the act of taking alcohol from a wine barrel (or something similar, like tapping a maple tree for syrup).
In your sentence example, it just means "depending on something" for livelihood, like children drawing money from the parent's account (because it is expensive to stay in the city).
In Chinese, "tapping into" has no direct translation, but the meaning is to 靠父母银行账户来维持生计.