A trading platform is a computer, a mobile, or a web application, which you can use to buy and sell financial assets. Almost all trading platforms are supplied with charting tools and all common technical indicators that you can add to the charts. Moreover, most common trading platforms are supplied with strategy back testers and automated alerts to help you automate your trading to some degree.
For trading platforms to work as they should, they need to have a fast connection to the server of the broker. The quality of this connection usually reflects on the quality of the execution.
The most common trading platform is MT4 and its later version MT5, which are supplied with almost features that a trader needs. However, some brokers offer you their trading services through their own proprietary platforms. Those platforms usually have a different interface design but do the same purpose, as they give traders access to the markets and enable them to view quotes and trade.
Moreover, most platforms enable you to install add-ons or plug-ins. For example, if you are a news trader, you can find the economic calendar add-on on MT4 and MT5 and install it, then plot it on your charts or beside them. You can also set up specific alerts depending on your strategy so that the platform gives you an alert when a certain event happens in the market (such as a MACD crossover).
In short, trading platforms can vary in their design of interface and tools, but they all must provide basic functionalities such as enabling you to enter and exit trades, setting up stop loss and profit-taking orders, and viewing charts. They are your portal to the global financial markets.