Pre-money is what the company is agreed to be worth before an investment lands; post-money is that number plus the money invested.
Raise $1M at a $4M pre-money valuation and the post-money is $5M — the investor owns 20%. Raise $1M at a $4M *post-money* and the pre-money was $3M, so they own 25%. Same headline number, five percentage points of your company.
This is the single most common place a first-time founder loses equity to a misunderstanding, because both parties can say "four million" and mean different deals. Always ask which one is being quoted, and always confirm it in writing.
Project types where this term stops being vocabulary and starts being a decision you have to make.