Emotions are complex things that take form in many ways and in just as many places. Emotions have a wide range, but why do we get emotional about things? One reason we can get emotional is if we're emotionally invested in someone or something. Essentially being emotionally invested in something means you can be hurt emotionally by something even if it isn't another human. I believe it extend further than just hurt and happiness, but that all depends on the level of investment and the form. For better or worse humanity finds ways to invest their emotions in many place and identify with things far beyond themselves.
Becoming emotionally invested in a TV show is quite simple and serves to enhance your enjoyment unless something goes wrong. Not every show has the capability to drag us in and toy with our feelings. For example, "Dora The Explorer" has a lower chance of getting you emotionally invested than a show like "Grey's Anatomy." The difference in character complexity and relatability as well as our ability to identify with situations allows us to care more. If the lizard in Dora fell off a cliff I wouldn't particularly care, but if a character I loved died on a show I enjoyed it would affect me in a different way.
Video games are another form of entertainment people where people often develop a sense of emotion. As with television, the content of a game very much effects how much we care about characters. Some games make it a point to introduce us to characters we begin to view in a way that transcends what they lack: physical form and identity.
Animals can easily grasp your heart; we wouldn't keep pets if we didn't have come degree of care for them. You have no emotional attachment to the bird that flew past you once a year ago, but the dog living in your house can be considered family.
This one should be obvious, of course we get emotionally invested in the people we love. Whether that love is romantic, familial, or for a friend does shape that investment, but doesn't change the importance. The well-being, opinions, emotions, and distance of our loved ones affects our emotions on a deep level.
The people we invest ourselves in aren't always close to us, we may never have met them. Some people care about their favorite celebrities and wish for their well being which is a form of attachment. Other times we instantly invest ourselves in people facing tragedy because the inherent empathy that often determines our humanity.
Emotional investment is something dangerous and beautiful, we open ourselves up for others and allow them to be an integral part of our world. Being afraid to form these attachments in any form isn't shocking, but emotions are a part of life and we shouldn't run from them.