Good question.
I'm looking at the Bitcoin chart, your first link...
The horizontal lines mark highe points (peaks) and low points (valleys) of the price that were hit before changing the direction of the trend.
The diagonal lines indicate different price movement trends. I believe there are two different sets of these trend lines, which indicates that the analysis is assessing the price trend based on different time intervals.
Finally, the arrows the author has written in is noting (first) the next high price trigger point, they're stating that if the price hits $2591 and doesn't exceed beyond it then we're at risk of a significant drop down to $1617.
These charts are applying technical analysis principles to the price of Bitcoin, these technical analysis principles can be applied to any investment that has price movement. The broad theory of technical analysis is that buying demand is driven by past and future price levels hit. You can infer the support or weakness for an investment based on what happens when the price hits or passes a previously high price point.
E.g., Bitcoin recently ran up to close to $3,000, then fell back to close to $2000, then quickly rebounded to $2,300. The fact that it rebounded to $2,300 sets a new level of support for the price. It's less likely that the price will crash unless it crosses below the $2,000 level again. Same applies to the $3,000 level in terms of price growth.
The quick summary for a long explanation is that new highs and new lows have funny affects on buying behavior.
Here's a link to an educational video on technical analysis:
https://www.youtube.com/watch?v=0XSMjhPKeb8