Assert the breadcrumb block (.breadcrumb) is, or is not, visible. Core renders no breadcrumb at all where the trail would be empty — the front page being the usual case — which is what the negative form checks.
Examples
Then I should see the breadcrumb
And we should see the breadcrumbs
Then should see the breadcrumb trail
And I should not see the breadcrumb
Then we should not see the breadcrumbs
Pattern
Then(/^(I |we )*should( not)* see the breadcrumbs?(?: trail)?$/, …)
Part of @webship-js/drupal-core-steps (github.com/webship/drupal-core-steps), a step pack for Webship-js 2.0.x.