The definition of tachycardia, according to a lot of sites on the Internet (do a Google search on the term) is any heart rate above 100 bpm. It poses a potential issue if the heart rate is elevated this high for a long period of time; it means that the heart doesn't have enough time to fill properly before the next beat, and may cause symptoms such as dizziness, etc. as well potentially damage the heart muscle in the long run.
Your heart rate will vary throughout the day. It'll probably be lowest when you first wake up, and it will definitely increase as the day goes on. When you eat, it may go up. When you get up after being stationary for some time, it will definitely go up, because the heart now has to pump more blood to other parts of your body which didn't need as much blood when you were stationary!
Well conditioned athletes can have heart rates in the low 40s, but this is rare. So you heart rate is nothing abnormal, unless it is accompanied by other physical symptoms such as breathlessness, dizziness, etc.
If you're not comfortable with what your doctor is telling you at the moment, you can switch, either to another doctor or a cardiologist/electrophysiologist who can do more "advanced" tests on you to put your mind at ease.
If you're wondering, my heart rate varies between 70s when I wake up to 80s when I'm awake during the day, then down to the 70s again three hours before bedtime, and may go into the high 60s before I sleep. I've done the ECG/EKG and my cardiologist said there was no need for further tests as my heart rhythm was normal, and my slightly faster heart rate was not giving me any other symptoms, although I do suffer from ectopic (or "skipped" or premature) beats now and then...