Let me jump in here :
The High, Medium and Low , This shows the amount of people actually Paying for clicks in their Adwords PPC Campains. If it is high then there is a lot op people that use this keyword in their campaign. This applies to the Medium and low too, where Low is you have a better chance of getting the Top Paid Spot with a lower Bid.
Usually when there is a High Competition this means that there is a lot of people that is already ranked and it will be almost Impossible to rank for that keyword on the first page of google in a short time.
So now you either spend a lot of money on the ppc or you spend a lot of time on seo to get fist page ( With time Im talking about a year of hard work building backlinks and unique content around the keyword).
So if the niche is very profitable and your getting a very good ROI on your PPC Campaign, it is much easier to just buy the top advertising spot or Bid the highest so you can get more clicks and sales on the product that you sell.
The Global and the Local monthly searches is an estimate on google's stat's that they have accumulated by taking an average on the monthly searches on that keyword over an estimated period of time.
This is just an estimate, so this can be greater or less. If something is trending then the number can be higher for 6 months because of an increase of searches in a specific time-span. It also helps to search that keyword in google trends just to see if it is still high.
So if your going to do PPC then you look for Keywords that has a lot of Searches and with a Low Competition.
If your doing SEO then Low Competition does help, but you will have to do additional research by searching in Google and then placing your keyword in "keyword" to see how many site's have that exact phrase on their pages( I usually look to find keyword's that have less than 50 000 here ) . then also you have to search and see how many people have actually optimized their pages for that Keyword by using the intitle:"keyword" here you will find all the website's that has this in their title and is actually optimizing for this keyword( I will usually look to find keywords that have less than 10 000 here)
If your trying to optimize for the US then you cant use your local google if your not living in US. you have to go to g**gle.com/ncr .
I Hope this helps
Good Luck
B