Meaning of ‘Check on’ Phrasal Verb in English

Can you check on the children to see if they are sleeping?

We should check on the progress of the construction project.

She checked on her email to see if there were any new messages.

Don't forget to check on the roast in the oven so it doesn't burn.

I need to check on my elderly neighbor to make sure she's all right.

I'll check on the availability of the product before placing the order.