The bid is the price at which the broker buys; the ask is the price at which the broker sells.
Every forex quote consists of two prices: the bid and the ask. The bid is always the lower of the two - it is the price at which the broker (or liquidity provider) will purchase the base currency from the trader. The ask (also called the offer) is the higher price at which the broker will sell the base currency to the trader. A trader opening a long EUR/USD position buys at the ask; closing that position (or opening a short) happens at the bid.
The difference between the two prices is the spread, which represents the broker's built-in transaction cost. On a quote of 1.08500 / 1.08502, a trader who buys EUR/USD at 1.08502 and immediately closes the position sells at 1.08500, realising a loss of 0.2 pips before price has moved at all. This is why traders need the pair to move in their favour by at least the spread width before a position becomes profitable.
Bid and ask prices update continuously in real time as the broker receives refreshed feeds from its liquidity providers. During periods of high liquidity - the London session and the London/New York overlap - the bid/ask gap is at its tightest. At session edges, during weekends, or around scheduled risk events, the spread widens as liquidity providers widen their own quotes. Understanding that the ask is always the buy price and the bid is always the sell price prevents the confusion that sometimes affects traders new to the two-price quoting system.