The Tenkan Sen (or turning line) is the sum of the high and low price then divided two (an average), over the last 9 periods. This takes into account the volatility of the security, because the range is used, as opposed to simply using the closing price like in a simple moving average.
The Kijun Sen (standard line) is the same formula just over 26 periods, with the same idea. Then the last line to understand, before understanding the cloud, is the Chikou Span (lagging line). This is simply price shifted back 26 periods. Considering that the Tenkan Sen is a faster average than the Kijun Sen, if the Tenkan Sen is above the Kijun Sen the trend tends to be bullish and the opposite for bearish.
The actual cloud part consists of two Spans. Span A of the cloud is the average of Tenkan Sen and Kijun Sen pushed forward 26 periods. Then Span B is the average range ((high+low)/2) for the last 52 periods pushed forward 26 periods. This is the future cloud that is beyond the current price.
If the price of the underlying asset is under the cloud the sentiment is bearish and therefore the opposite for bullish. If cloud Span A is below Span B, the sentiment is bearish. Span A over Span B would imply bullishness.
This study is immensely popular in Japan, the same place where candlestick studies were developed. As a result, many Japanese based securities follow the Ichimoku Cloud given its roots in the country and its popularity. Yen based currency pairs, Nikkei 225 futures and Japanese equities are just some of the assets that respect the Ichimoku Cloud.
In a concluding note, should AAPL close above the cloud today…this would mark the fifth day in a row price has closed above the cloud. This may indicate a major trend reversal. Furthermore, the Tenkan Sen 9 period line has moved up and over the cloud and presently sits around $440.61…potential support.