Q:

What's causing the 'wait' time before my HTML loads? 

I have a website the seems to load very slowly.  When I run a speed test on it I see there seems to be a 6 secound gap before the HTML loads.  Images and JS scripts load very fast after that point. 
You can see in the pic below the yellow 'wait time' bars:

This seems to be consistant no matter what the HTML content on the page is. 
This site is using a CMS (ModX Revo) so HTML is actually stored in an SQL database and brought forth by PHP, but I've never experienced this issue before. 
Would anyone know what is causing this and how I could speed it up? 

A:

The technical term for waiting is refereed to as time to first byte and determines the  responsiveness of a web server or other network resources.  
Some common reasons you might see an high time to first byte:

Overloaded network (normally shared hosting)
Misconfiguration servers
Distance from you and the server (geo location plays a minor role)
Server errors (hops)

Generally this problem is often seen in shared hosting because of the sheer amount of websites and people visiting them which of course increases the network byte time.  Another possible cause is an error on the network somewhere, like a hop or because your server is not within the location of your targeted audience, for example a 'GOOD' UK server will have a lower byte time than a US server targeting users in the UK, because of the distance that the data needs to be sent and received (Normally a increase of around 100-200ms). 
Maybe a time to get a new host
In the past I have to move from server to server because of the lag of the time to first byte, you may be in the situation of having to choose a new web host or upgrade your current package. 
Reliable testing
Testing the speed of your website from your home broadband is very biased because it may be a problem with your broadband not responding to the website.  You should test your website using multiple connections from multiple servers... I recommend web page test and running multiple tests at once from different locations and many in the targeted geo audience.  This will give you a better overview of whats going on, if its first byte then I recommend you contact your web host before anything else. 
Pinging and trace route the server
If you attempt to run a ping on the server the results may display or may not, ping uses ICMP rather than UDP or TCP meaning its not like querying the server on port 80 which your httpd will be running on.  You could use trace route to identify any servers on the route that could be causing the first byte to increase, again... it does not query the httpd server on port 80 and if traceroute using Windows it'll use ICMP and Mac/Linux machines will use UDP.  It's worth testing because its such a quick and easy thing to do but if the results come back fine, doesn't necessary mean there isn't a problem somewhere. 

A:

1) You have Adobe TypeKit which is not loading asynchronously with the current code.  Try replacing it with the advanced asynchronous code:
http://help.typekit.com/customer/portal/articles/649336-embed-code

This standard embed code takes advantage of the fact that 
  tags block further rendering of the page to help prevent the FOUT
  [Flash of Unstyled Text].  While the Typekit script is loading,
  rendering of the page is blocked, so text won’t start to render with
  fallback fonts. 

2) Test with new TypeKit.  How is the loading time now?  Better?  Go to step 3. 
3) Replace your Google Analytics with an updated JavaScript that provides the latest asynchronous syntax: https://developers.google.com/analytics/devguides/collection/gajs/
4) Test.  Is the page loading better still? 
5) Finally, consider optimizing images such as pattern.jpg.  I converted it to a PNG and was able to reduce the file size from 199kB to 56kB. This reduces the time to receive the file: https://www.dropbox.com/s/i06jx509bmprhhh/pattern.png?dl=0
I hope this helps. 

A:

PHP vs. Non-PHP Elements
If you compare your non-PHP asset load times to your PHP based load times, you will see that the server responds quickly if PHP is not involved.     
This typically indicates an issues internal to your PHP script.   
The problem could be within the PHP layer or the database.   Using advanced debugging tools like XDebug or NewRelic can help you quickly spot the bottleneck. 
Time to first byte issues can be caused by hardware constraints, poor configuration or inefficient code.    On shared hosting, hardware constraints and poor configuration are most likely. 
In any case, solving the issue usually means one or all of:

More hardware
Better programming
Add Caching

Faster hardware is an obvious but often costly solution if you are already on dedicated resources. 
Better programming may not be possible if the problem is internal to code you don't maintain or lack developer resources.  
Caching helps by reducing the number of requests that must hit the underlying, poorly performing resources.   
Testing
When using testing tools be sure to do multiple runs.   Network and temporary server spikes can easily lead you down the wrong path, so you want to try to average these out. 
Hosting
If you are on a shared hosting account, then consider moving to cloud or VPS type services so you have better insight into performance issues.   Unless you use a caching technique (CDN or Cloudflare type service), correcting performance issues on mass shared hosting systems can be very challenging as you lack sufficient control of the server. 