Outside my house, off sidewalk, are three metal cases. One is called a 'joint trench'. I have no idea what they are for. My cable TV and internet are attached I believe to similar cases but on other side of street. One of the cases says 'telecommunications'.
The joint trench one had its lid blown off during a wind storm but I kicked it back on.
Any idea what these cases are for?

They are for the three utilities each home uses, CATV, telephone, and power. The 'cases" are called hand holes, and are used for pull points and distribution points for the utilities.

If here are any covers loose, call the appropriate utility company, and they should be glad to hear from you and come out and secure the covers promptly.

Perfect answer from a pro. Thanks!