what does "gut tightened a little"mean?
“Mr. Landon, this is Sherrilyn Burke, Burke-Massey Investigations.”
“Yeah.” His guts tightened a little, anticipation and dread. “It’s good to hear from you.”
“I have a report for you. I could e-mail it, but I’d like to go over it with you in person. I can come out to you tomorrow, if that’s convenient.”
“Is there something I should worry about?”

Question

what does "gut tightened a little"mean?
“Mr. Landon, this is Sherrilyn Burke, Burke-Massey Investigations.” 
“Yeah.” His guts tightened a little, anticipation and dread. “It’s good to hear from you.” 
“I have a report for you. I could e-mail it, but I’d like to go over it with you in person. I can come out to you tomorrow, if that’s convenient.” 
“Is there something I should worry about?”

Answer

"Gut tightening" is a literal term. It refers to the feeling in your stomach when anxious/nervous/stressful/in anticipation.

Fun fact: the reason for this is that when under stressful situations, your body goes somewhat into the 'fight or flight' response, and prioritises blood flow to certain areas of the body. The tightening in the gut is one of the resulting side effects :)