This post does a good job of characterizing the good kind of intellectual humility (recognizing that you might be wrong and using that to better pursue the truth), but I think there is also a good kind of social humility (or "social modesty," if you prefer that label). Not asserting high status, or taking too much credit, or claiming privileges can be an important part of cooperating and working well with others.

For instance, people tend to see themselves as more responsible for their successes than their failures (self-serving attributions), which can be a problem if a group of people working together on a successful project all want to take personal credit for it. Social humility can help restrain that urge to take credit so that the group can work better together. And when someone from the group is talking with people outside the group, there's a temptation to try to reap a larger social benefit by claiming personal credit for the group's success. This can undermine the group's cohesiveness since they're now competing for credit and not just pursuing a shared goal together, and they can avoid that problem by cooperating on how they present themselves to the outside world and agreeing to share credit with the whole group (like a humble athlete who credits his teammates).

People often talk of being humbled by success, and part of what that involves is an impulse to share credit with the other people who contributed to your success ("I couldn't have done this without..."). Presenting yourself humbly, rather than as someone who's just better than everyone else, can make your success seem more accessible to other people and encourage them to follow in your footsteps. It also makes you seem more approachable, which is good for you too since if people are too intimidated to have open discussions with you then it can be hard for you to learn (there's a Feynman story about that).

There are bad forms of social humility, too, like the version that makes someone not want to excel because it'll just be awkward. But there is a good kind of social humility which is an important part of managing social relationships. And it's relevant to science too, as long as you include the parts of science that involve working collaboratively with other people or encouraging others to pursue truth.