Technically known as 'lateral epicondylalgia', tennis elbow can be a very painful condition that affects the common extensor tendon as it attaches into the lateral apsect of the elbow. In its early stages it presents as inflammation around the insertion of the tendon, but as time passes this inflammation subsides despite the pain lingering. Scans may sometimes show a thinning of the tendon density (a process known as 'tendinopathy') that progresses on to more distinctly visible tears of the tendon. For many years it was thought to be an overuse syndrome, but recent research tends to suggest that the injury may relate more to a long term 'underuse' scenario. Confused?
Consider this example: a boilermaker works for 10 years in the same job, a physically demanding but repetitive role. Over that time, his forearm musculature and tendons become accustomed to that loading and remain strong for the demands placed on him. Unrelated, he then decides to take time off work to build a pergola at home and dig a large garden bed over the course of 6 weeks or so. He's never been an avid gardener, so all of a sudden his forearm is now being subjected to a number of very different actions without first being conditioned into them. He develops 'tennis elbow' because of the change in the type of loading, effectively because over the preceding 10 years he had 'underused' his arm relative to the demands he has now placed on it.
So why is it called tennis elbow? Well, tennis players do get the problem too! A combination of a large racquet handle and repeated micro-trauma from back hand shots are thought to contribute in their case.
A golfer's elbow is a similar condition but it instead affects the inner (or flexor) aspect of the elbow. As such it is called 'medial epicondylalgia'. The process by which it arises is likely very similar to its lateral counterpart, but because it is seen less frequently there has been considerably less research done on it at this point in time. But yes, golfers can get it too!