An old-timer is someone who's been around a long time and has experienced a lot. When you get a new job, the old-timers there are the ones who can show you how things are done.
Old-timers are veterans — they're been through it all. The old-timers in a busy office might reminisce about the days before computers, when everyone used typewriters and Rolodexes, and the old-timers in your neighborhood can tell you how quiet it used to be. You can also use this noun to mean "elderly person," like your grandpa and his buddies: "There are so many old-timers at the gym lately, I can never find a free treadmill."