Eş is spouse (unisex); karı is wife – as opposed to koca, husband.

''Karım'' means exactly ''my wife''

But ''eşim'' means both wife and husband. 

So you can call your husband as ''eşim'' and your wife as well. It's like spouse.

If you are a man you call your spouse as Karım 

but if you are a woman you call your husband as kocam 

but you can use " eşim  " for both husband and wife.