In short: A currency is the money that a country or a union of countries (such as the euro area) has declared legal tender — prices are counted and taxes are paid in it.
Simply put: A currency combines three things: a unit of account (what we count prices and debts in), a means of payment (what we settle bills with) and a border (whose central bank and whose laws stand behind it). There are about 155 currencies in circulation according to the ISO 4217 list. Some countries have no currency of their own and use a foreign or shared one. A currency's value against others — the exchange rate — reflects trust in it.
Example: At a fictional rate of €1 = $1.10, €200 should buy $220. But an exchange office earns on the gap between its "buy" and "sell" rates, so you receive less.
Watch out: Myth: "A strong currency means a strong country." A currency that has risen a lot makes exports harder. A strong currency is one people trust.
Source: ISO 4217 (SIX) — https://www.six-group.com/en/products-services/financial-information/data-standards.html · ECB, "What is money?" — https://www.ecb.europa.eu/ecb-and-you/explainers/tell-me-more/html/what_is_money.en.html