The term "hedge" in investing means to invest in some way that will protect you against some particular eventuality that you fear. You try to invest in ways that will not lose value if that thing happens. So a hedge against inflation is an investment (or an investment strategy) that will protect you against inflation.
There are many different ideas about how to hedge against inflation. A common one involves buying something like gold or art or real estate. These are things whose value is supposed to go up at roughly the same rate that inflation does. Because of this, the investor who buys them will not lose out if there is inflation.
Hedging refers to protecting oneself against any sort of risk. If an investment is made by buying stock or government securities, the returns are in the form of dividends or an appreciation in the value of the stock or as interest that one receives from government securities.
When the risk is inflation or depreciation in the buying power of money, different assets have to be bought as a protection. The favorite assets for this have been gold, property and in recent times Inflation-indexed securities. These assets increase in value in close correlation to the value of money. Hence they can be used as a hedge against inflation.
In economics, business and, particularly, trading of all types, hedging refers to a method of reducing risks by taking action that tends to counter the affects of future variations in environment, particularly in price of some asset like shares, foreign exchange, or some commodity. In particular hedging refers to practice prevalent in trade exchanges dealing in all kinds of assets to reduce the risk of losses because of price fluctuations. It is important that while a hedging action protects from possible losses due to future price fluctuations, simultaneously it also eliminates possibilities of gains from corresponding price variations.
The term inflation generally refers to general level of price rise covering entire collection of goods and services used in the economy, rather than price rise in some selected products. I am not aware of any standard methods of hedging against such general inflation. I believe the question has used the word inflation to mean price rise of specific assets rather than a general increase in price levels in an economy.
Hedging against price rise in future is required when it is known that some assets will need to be purchased in future. For example, a company which has imported goods for which payment will become due in foreign currency some time in future, say after 90 days from the date of placing order. In this case the company will have to buy foreign exchange in the required currency after 90 days. If the rate of this particular currency rises in future, the company will need to pay extra money for purchasing the currency. The company can reduce this risk by purchasing the required foreign currency in a futures transaction where the purchase takes effect after 90 days at an agreed rate.
If the actual rate of required currency increases after 90 days the company will still be required to pay for the currency at the rate agreed earlier. This way it will avoid the possible losses due to increase in price. But the company will also loose the opportunity to benefit from the future price falls. Even if the price of currency falls below the rate agreed, the company will have to buy the currency at higher rate agreed earlier.