There are several messages you can get from this sonnet, but I think I'll stick with the one that makes most sense to me.

In order to get an idea of what the sonnet means, we have to look directly at it.  It is common to interpret this poem in terms of quatrains (groups of four lines) but that doesn't seem natural to me.  To me, the poem must be read "from head to toe."  That makes it harder to understand, but I think we'll manage alright. We'll just stop every few lines to check our understanding, okay?

Let's start!

"They that have power to hurt and will do none,

That do not do the thing they most do show,"

What the heck does this mean?  It appears to be talking about people who have power over others, power that could be harmful.  The second line implies that those in power do not exercise it to hurt others, even though they could and even though they look tough on the outside.

"Who, moving others, are themselves as stone,

Unmoved, cold, and to temptation slow,"

These people of power are able to influence others but themselves are not easily moved, do not display their feelings, and do not respond quickly to temptation.

"They rightly do inherit heaven's graces.

And husband nature's riches from expense;"

These people inherit grace from heaven, and are able to grow riches from the expense of energy required to remain uninfluenced and true to their values.

"They are the lords and owners of their faces,

Others but stewards of their excellence."

These people own their actions and control them.  Other people, who do not, are only "stewards" (caretakers) of their emotions, not owners of them.

"The summer's flower is to the summer sweet,

Though to itself it only live and die,"

Now it switches images. We are not talking about people, but rather nature.  A flower during summer smells sweet, but is not sweet to itself (the flower is indifferent to its own sweet smell.)  The flower is "born" and it will "die," that's what it knows.

"But if that flower with base infection meet,

The basest weed outbraves his dignity:"

The flower is easily made sick...the weed, an ugly, stinky flower, will outlast it because it is more hearty.

"For sweetest things turn sourest by their deeds;

Lilies that fester smell far worse than weeds."

This is a great last line.  Something that starts out as beautiful on the outside has a far greater penalty when it doesn't live up to expectations.  The dead flower will stink worse than the dead weed.  What he seems to be saying is that even if something appears to be beautiful and righteous on the outside, because of its actions you may find it is far worse than something that is not so "flashy" in its actions.

How does this tie in with the first image?  The powerful individual is not flashy at all.  He is stoic.  You cannot read him by his face, which is grim and cold.  It is by his actions that you know he is a man in "grace."  He does not do good to get attention or for appearances.

The flower looks and smells beautiful, but because of its actions it ends up stinking.  It is unaware of its actions, and does not master them. In the end, it is the tough weeds that both outlive and smells less than the attractive but weak flower.  Both the man and the flower images are used to let the reader know that outward appearances can be deceiving and should not be trusted.

Like I said, there are other explanations, but this is the one I like.

Shakespeare's Sonnet 94 seems at first to have two unrelated parts.

In the first part (first 8 lines) Shakespeare praises people who are stoic -- those who can remain in control of themselves at all times.  They are the ones who will rule the earth and others will just work for them or take care of the things they produce.

The second half of the sonnet seems to be talking about nature.  He says flowers are beautiful in themselves but that they sort of have responsibilities because they are of value to nature as a whole.  If they don't live up to those, they are worse than weeds.

So what does it all mean together?  It's social commentary.  The second part is really also talking about what people should be like.  The people who are high-born (the flowers) need to help society and not just look pretty.  Otherwise, they are worse than the low-born "weeds."