This is the chart of Tesla today. In this article, the analyst says Tesla stock has a resistance at 780 and there will be breakout if the stock breaks that level.
From Wikipedia:
A breakout is when prices pass through and stay through an area of support or resistance
In this case the analyst is predicting that Tesla will "break out" of the pattern and continue to trade (price-wise) above the previous level of resistance.
What technical factors cause the stock to breakout?
Nothing causes a breakout. It's just a pattern that sometimes happens.
The analysts have drawn a 200 Moving Average here. Are they for investors guidance so they all can invest at the same time?
If you mean that all investors will trade when the 200-day MA hits the resistance level, then no. It's just showing that the stock is trending up. It's simply another indicator that can interpreted however you want.
