It means to continue believing that something good might happen, even when it seems unlikely.

nadati se, vjerovati, ne gubiti nadu

<span class="sentence" aria-label="families still held out hope that they would be found alive.”>

<span class="sentence" aria-label="The scientist held out hope that one day, she would discover a cure for the disease.”>

<span class="sentence" aria-label="After months of job applications, Sam held out hope that he would finally get an interview.”>