How to trigger Jenkins builds remotely and to pass parameters

In your Jenkins job configuration, tick the box named "This build is parameterized", click the "Add Parameter" button and select the "String Parameter" drop down value.

Now define your parameter - example:

Now you can use your parameter in your job / build pipeline, example:

Next to trigger the build with own/custom parameter, invoke the following URL (using either POST or GET):

http://JENKINS_SERVER_ADDRESS/job/YOUR_JOB_NAME/buildWithParameters?myparam=myparam_value

See Jenkins documentation: Parameterized Build

Below is the line you are interested in:

http://server/job/myjob/buildWithParameters?token=TOKEN&PARAMETER=Value