A hedge fund is an investment vehicle where investors inject capital into a specific investment strategy that is actively managed by a hedge fund manager.

Hedge funds are known for their unique trading strategies ranging from heavy use of algorithms to shareholder activism (seeking to control corporate actions) to short selling.

Equity refers to the asset class of equity i.e. Stocks.

Long refers to buying a stock in which case you make money when the stock price goes up.

Short refers to shorting a stock in which case you make money when the stock price goes down. To short a stock, you start by selling a stock you don’t currently have and then taking on an obligation to buy back the stock at a later date.