An algorithm is defined by Merriam Webster as a procedure for solving a mathematical problem in a finite number of steps that frequently involves repetition of an operation; broadly :  a step-by-step procedure for solving a problem or accomplishing some end especially by a computer.  When applied to the idea of Forex trading this means that a computer is set to follow specific instructions in order to execute the trades.  This allows a trader to remove all emotion, human error and need to be awake from his trading.

Algo-systems are a programmed set of instructions that create trade signals that can execute trades instantaneously and include position sizing and exit commands.  This translates to being able to watch profits come in and out of your accounts without actually doing anything.

Computer systems, when given specific instructions can do complicated calculations that would take humans much longer and without the concern of human error.  This is the reason that algorithmic trading has become more and more popular lately.  People are more computer savvy than ever before and are therefore more comfortable having computers do their trading for them based on algorithms that the trader or brokerage creates.

Algorithmic trading takes place at a time and pace that might not be realistic for most people.  Those are some of the big advantages to this type of trading.  Algo-trading as it is often called, allows for instantaneous trading which can mean that the price changes that could happen between when a person decides to make the trade and actually executes the trade would not be a factor.

Algorithmic trading is very efficient which can lower the costs of trading.   When there is little or no actual human hours spent on the trading the expenses involved in the trading are less than with a personal broker.

The formulas you are using in your algorithm can be tested with historical data.  You can basically go back in time to see if your plan would have made money and how much which will go a long way in deciding if it will be successful for you.

The pace at which algorithmic trading can happen makes it perfect for High Frequency Trading.  This means that trades can take place within milliseconds of price changes which can be advantageous to some traders. There are many different types of algorithmic trading in Forex.

Just as there are many advantages to Algo-trading, there is a downside too.  There are many experts who worry about the overall effect of this type of trading on the market.  There is significant concern about what could happen in a turbulent market and then what the result of people suspending their algorithmic trading during that turbulence could cause.

Spikes in volatility when many traders using algo-trading all do the same thing at one time can cause problems in the Forex market.  The opposite situation could also cause difficulty for the majority of Forex traders.  If there is less movement during times of market stress, it could mean that short-term traders do not do as well.