In times of happiness, despair, love, or even hatred, having someone to share these experiences with is always comforting.
The literal meaning of this saying simply indicates that one should hold on dearly to the friends they have. I believe that friendships, as easy as they are to make, are sometimes challenging to maintain. Some of the friendships that we form or develop throughout our school years are circumstantial. Dismissing the idea of solitude and isolation, we are quick to associate ourselves with people we feel we can relate to. What this results in is an invisible barrier that stops you from seeing these people as a whole, but rather the convenient parts that fit with the idealized friendship that you wish for. And when your ways separate, it's not long before you outgrow each other.
Obviously, I'm not saying that this is the case 100% of the times; good friendships can emerge from a school environment — personally, the people I call my friends are the people I spent the majority of high school with. It's a matter of drawing a line between the people you hang out with, and your real "friends."
The figurative meaning of this quote is found in the roots of Nigerian culture. In Nigeria, as well as other African countries, the left hand is associated with "bad" (unclean or messy business, bad luck, etc.) and the right hand is, therefore, the "clean" hand. To hold your friend with both hands also implies that you are there for them through the good and the bad. Similarly, when we hold hands, the two (left and right) grasp each other, the positive and negative joining together and canceling out.
Real friends are a blessing to have. They will support you or advise you during your stupid moments. They'll make you laugh until your stomach hurts, build some of the best memories in the span of a few years. These friends will have your back no matter what, be happy for your Wins, and mourn with you in your major Losses (depending on the type, they might actually make fun of you). In a fight, these people will never jump on the opportunity to spill your secrets or talk about you when you have your back turned. These "real friends" eventually become family. And family is not only an important thing, it's everything. So, cherish these friends, we don't get 100 of them.