you'll pass (something) on your (right/left)

This is a phrase to use when you're giving directions. Use it to tell someone what landmarks they should see when they're driving. These landmarks let the driver know if they're going the right way. Here are some other examples:

Drive in that direction for about 15 minutes. You'll pass a big pond on your right. After that, there'll be a stop sign.

Go down 14th street for 4 blocks. You'll pass a Shell station on your left. Look out for Montgomery St. Take a left on Montgomery and it's the 4th house on the right.

veer off to the (left/right)

To "veer off" means to turn slightly. Telling someone to "veer off to the left" is different from telling them to "turn" to the left. In a car, a "turn" usually requires you to stop, but "veering off" doesn't. Here's a picture that illustrates the difference:

Look at the map above. If the speaker told his brother-in-law to "turn left after the coffee shop", he would choose to turn on the street that the car is placed on instead of the correct street.

The word "veer" can be used in other situations as well. It's not just for cars. Storms can also "veer off":

They were expecting the hurricane to hit the South Carolina coast, but it veered off and didn't hit until Virginia.

When someone drives their car off of the road accidentally, we say that they "veered off the road":

Barry fell asleep at the wheel, veered off the road, and crashed into a telephone pole.

Since "veering off" means that you're not going straight in one direction, people use it to describe things that are not happening in the way that was expected, like a conversation:

The conversation suddenly veered off into the topic of birth control.