I can tolerate (something)

To "tolerate" something that you don't like means that you put up with it. You let it happen, even though you don't like it.

If there's something that you don't like, but you're able to accept it reluctantly, say "I can tolerate ___":

A: Do you eat shrimp?

B: I can tolerate it, but I don't love it.

I can tolerate a long commute as long as I'm able to get a seat on the train.

When you use the word "tolerate in a negative sense, though, it has a stronger meaning. You use "can't tolerate ___" to talk about things that you not only dislike, but also make you angry:

I can not tolerate laziness.

I can't tolerate people who brag.

As in these examples, "can't tolerate ___" often describes people's behavior.

(someone) can't stand (something)

Talk about something you don't like at all with the phrase "I can't stand ___":

I can't stand olives!

I can't stand being apart from you for so long.

I can't stand people who make racist jokes.

I can't stand to see an animal in pain. 

You can talk about other people with this phrase as well:

Some people can't stand losing.

She can't stand it when people talk while they're chewing their food.

It's not that common to use "stand" this way in positive sentences. Instead of saying that you can stand something, say that you can "tolerate" or "handle" it:

A: Do you like rap music?

B: Yeah, it's not my favorite but I can usually tolerate it.

what (clause) is (something)

The example at top could also be said this way:

I can tolerate the heat, but I can't stand this humidity!

Using "what I can't stand is ___" places more emphasis on the thing that the speaker doesn't like. It makes the sentence sound like a more forceful complaint. Here are some more examples:

I'm OK with working late hours from time to time. What I don't like is my boss expecting me to do that with no overtime pay and no appreciation for my effort.

I don't want to hear your excuses. What I want from you is an apology.

heat / humidity

"Humidity" is the amount of water that's in the air.

People like to compare the "heat" and "humidity" of the air, because air that's hot but dry isn't as bad as hot and humid air.