“Why don't you send in your résumé and see?”
Your husband is telling you about a job that he saw a posting for. He says that he would like to get that job, but he doesn't think he's really qualified for it. You think that he should try anyway because there's a possibility that he could get the job. This is your suggestion.
Why don't you send in your résumé and see?
This is a friendly way of suggesting that someone do something. You can use this phrase with anyone who you feel comfortable giving advice to.
Also be aware that this phrase can be used in a rude and angry-sounding way:
Why don't you shut the hell up?
Usually, if you are suggesting things that are positive and that the listener agrees with, you don't have to worry about sounding rude of angry.
To "send in" something means to submit it by mail or email. It's similar to the word "submit", but "submit" can also be used to describe giving something to a person by hand, whereas "send in" cannot.
You "send in" a résumé, an application, a payment, or some other official document. You submit it to someone who has authority.
This phrase can be ordered two ways: "send ___ in" or "send in ___":
Have you sent in your application yet?
I sent my rent check in last week.
But always put "it" and "that" before "in":
I can't remember if I sent it in.
A résumé is a document that lists your work history, your education, and your accomplishments. It's usually one or two pages long. People submit résumés to companies when they are trying to get a job.
Usually people have just one résumé, so it makes sense to refer to it as "your résumé" or "my résumé" instead of just "a résumé".
This means to try doing something in order to test the results. The phrase "send in your resume and see" means to submit your resume and then wait for the results. The phrase "and see" is most commonly used with "try it":
A. What does this button do?
B. Try it and see.