This proverb uses vivid imagery to illustrate the unpleasantness and irritation a lazy person causes to those who depend on them. Let's break it down:

"As vinegar to the teeth..." Vinegar is acidic and can cause a sharp, unpleasant sensation when it comes into contact with teeth.
"...and as smoke to the eyes..." Smoke is irritating and painful to the eyes, causing them to water and sting.
"...so is the sluggard to those who send him." A "sluggard" is a lazy or idle person. "Those who send him" are the people who give the sluggard a task or responsibility, expecting them to fulfill it.

Meaning:

The verse means that having to rely on a lazy person is a frustrating, painful, and ultimately unproductive experience. Just as vinegar to the teeth and smoke to the eyes are irritating and harmful, a sluggard's laziness causes discomfort, frustration, and often delays or ruins the work for those who depend on them.

In other words, the proverb is saying:

Depending on a lazy person is like a constant irritation.
Their laziness causes problems and frustration for the people relying on them.
It's a warning against being lazy and a reminder that our actions have consequences for others.
It highlights the value of diligence and hard work.

The proverb emphasizes the discomfort, irritation, and ultimately the negative impact that a lazy person has on those who have entrusted them with a task or responsibility. It is a warning against laziness and a call for diligence and responsibility.