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Question about QG omega equation in Holton's book

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I am a layman to meteorology and I am studying some basics using Holton's book, An introduction to dynamic meteorology (4th ed). Now I am with the Omega equation which is section 6.4.1 in that book. I can go through the derivation of the Omega equation but I find difficulties in understanding the exmaple used to explain the role of the advection of absolute vorticity by the thermal wind in forcing the vertical motion. The example is shown as following:


In the content, it says "Due to the westward tilt of the system with height, the 500-hPa geopotential field leads the isotherm pattern." What do the terms "westward tilt" and "lead" mean? It also says "At 500 hPa the positive relative vorticity advection is a maximum above the surface low, whereas negative relative vorticity advection is strongest above the surface high." I am confused from where we can draw this conclusion? I know these might be common sense for the seasoned meteorologist, but it will really help me a lot if anyone could figure it out. Thanks.:)

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