What does server.error.include-binding-errors=on-param in Spring do?

To begin, what I did is to do a global search on server.error.include-binding-errors in the library, which lead me to spring-configuration-metadata.json

    {
      "name": "server.error.include-binding-errors",
      "type": "org.springframework.boot.autoconfigure.web.ErrorProperties$IncludeAttribute",
      "description": "When to include \"errors\" attribute.",
      "sourceType": "org.springframework.boot.autoconfigure.web.ErrorProperties",
      "defaultValue": "never"
    },

We see the related attribute is errors here, and the value class is IncludeAttribute. By checking the documentation in IncludeAttribute#ON_PARAM

public static final ErrorProperties.IncludeAttribute ON_PARAM
Add error attribute when the appropriate request parameter is not "false".

We know that the errors attribute will be added when there is a request parameter that is not "false".

If you want something concrete, let's consider the following example:

Controller

import org.springframework.web.bind.annotation.PostMapping;
import org.springframework.web.bind.annotation.RequestBody;
import org.springframework.web.bind.annotation.RestController;

import javax.validation.Valid;

@RestController
public class TestController {
    @PostMapping("/dummy")
    public String test(@Valid @RequestBody DummyDTO dummyDTO) {
        return "";
    }
}

DTO

import javax.validation.constraints.NotNull;

public class DummyDTO {
    @NotNull(message = "mandatoryText can not be null")
    private String mandatoryText;

    private String canBeNullText;

    public String getMandatoryText() {
        return mandatoryText;
    }

    public void setMandatoryText(String mandatoryText) {
        this.mandatoryText = mandatoryText;
    }

    public String getCanBeNullText() {
        return canBeNullText;
    }

    public void setCanBeNullText(String canBeNullText) {
        this.canBeNullText = canBeNullText;
    }
}

Suppose we set
server.error.include-binding-errors=on-param

When we run with parameter errors=false

curl -H "Content-Type: application/json" --data '{"canBeNullText":""}' -X POST http://localhost:8080/dummy?errors=false

the result will not include errors

{
    "timestamp": "2021-06-11T13:38:29.868+00:00",
    "status": 400,
    "error": "Bad Request",
    "message": "",
    "path": "/dummy"
} 

When we run with parameter errors=true

curl -H "Content-Type: application/json" --data '{"canBeNullText":""}' -X POST http://localhost:8080/dummy?errors=true

the result will include errors as

{
    "timestamp": "2021-06-11T13:51:00.649+00:00",
    "status": 400,
    "error": "Bad Request",
    "errors": [{
            "codes": ["NotNull.dummyDTO.mandatoryText", "NotNull.mandatoryText", "NotNull.java.lang.String", "NotNull"],
            "arguments": [{
                    "codes": ["dummyDTO.mandatoryText", "mandatoryText"],
                    "arguments": null,
                    "defaultMessage": "mandatoryText",
                    "code": "mandatoryText"
                }
            ],
            "defaultMessage": "mandatoryText can not be null",
            "objectName": "dummyDTO",
            "field": "mandatoryText",
            "rejectedValue": null,
            "bindingFailure": false,
            "code": "NotNull"
        }
    ],
    "path": "/dummy"
}

References:
Implementation for web reactive
DefaultErrorWebExceptionHandler#isIncludeBindingErrors
AbstractErrorWebExceptionHandler#isBindingErrorsEnabled

Implementation for web servlet
BaseErrorController#isIncludeBindingErrors
AbstractErrorController#isBindingErrorsEnabled