“Make sure to bundle up!”

It's cold outside and it's been raining recently. You're chatting with another mother at your child's daycare center. You're both leaving now. You want to say something nice to her as you leave, so you warn her to dress warmly:

Make sure to bundle up!

Make sure to (do something)

To "make sure" means to check something again, so that you know that it's OK. When you want something to happen and it's important, you check to "make sure" that it happens. For example, before your house guests leave, you can tell them:

Make sure you've got everything.

Or when someone is grilling some meat:

Make sure they're cooked all the way through.

A more formal version of this phrase is "make sure that (clause)":

Make sure that the pork chops are cooked all the way through.

But you can also follow "make sure" with the "to" version of a verb:

Make sure to take everything home with you.

Make sure to cook them all the way through.

bundle up

To "bundle up" means to dress warmly in cold weather. Someone who "is bundled up" probably has on a jacket, scarf, gloves, and a winter cap.

Telling someone to "bundle up" sounds like something that a mother would say to her child. So the feeling that this phrase communicates is warm and caring.