The covalent bond is central to the study of chemistry. It’s not the only kind of bonding (compounds can exhibit ionic bonding as well, and metallic elements and alloys exhibit metallic bonding), but covalent bonds hold together non-metal atoms into the elegant and beautiful structures we call molecules that constitute the bulk of our field. No covalent bond means no molecules. No molecules means pretty much everything is physics.
Like most chemists, I am kind of touchy about how to describe a covalent bond. My best description is that it is a force between two atoms created by the mutual attraction for shared electrons. Those electrons are only shared because of the laws of quantum mechanics which places them (mostly) in a position between the atoms they hold together. Unfortunately, the notion that a bond is actually a force, not a physical thing, is hard to think about. How do you draw a force? We have mostly settled on using lines between atoms to signify that this force exists between them. Many molecular models use sticks to hold atoms together into molecules. This is leads the novice into thinking about atoms held together by sticks, not forces, which leads (in part) to my next problem.
Many students will tell you that breaking a bond releases energy, but the opposite is actually true. Many people blame the biologists for this because of the emphasis on the hydrolysis of ATP which releases energy. ATP hydrolysis does cleave an O to P bond but it also forms hydrogen bonds, and the formation of those hydrogen bonds are the reason that energy gets released.
However much blame the biologists receive (or deserve), there is another reason for this misconception. Breaking a bond is not like breaking a stick at all. Because a covalent bond is an attractive force, you must put energy in to overcome that force. The correct analogy here is pulling magnets apart, not breaking a stick. Sadly, because students focus not on bonds as a force (which we say) but rather as bonds as sticks (which we show them), the concept gets messed up in the process of trying to learn it.
I try to emphasize this in class by putting magnets in the hands of my students on the first day we discuss covalent bonds. Whether or not this helps is arguable given them number of students who tell me the wrong answer on exams when I ask about whether or not breaking bonds releases or absorbs energy. However, it is desperately important for teachers and students to think about these issues when covering this most central of chemical concepts.