I wear a heart rate monitor during most workouts, and I have owned two Polar monitors over the years, which I recommend highly--don't go with any other brand, if you get one. You don't need one of the crazy model that has ridiculous bells and whistles built into it. You basically want something that gives you a reading on your heart rate, keeps time and records the results from your workouts.
Yes, you can run or bike or do other cardio work without a heart rate monitor, but if you get serious about the kinds of workouts you do and want to introduce variety to challenge your body and get better results, a HR monitor is a great tool. It's pretty much a necessity for endurance and interval running and biking. It has helped me pace myself and vary workouts from day to day to allow myself to keep at it, while occasionally giving my body the time it needs to recover.
If your goal is losing weight, which I gather from your post, a HR monitor is a simple way to make sure you get your heart rate into a good, steady zone. It takes guesswork out of the equation. Just try for somewhere around 60 to 70 percent of your target rate for a half hour or 45 minutes a day. That way you start working yourself into shape, without making your workouts so miserable that you quit before you get started.
Your target rate is based on age and weight, but don't go entirely by the chart. This is where a HR monitor helps you learn yourself and steady your workouts based on how you have performed in the past. I can sustain a higher heart rate for longer periods than my age and weight would suggest, so I calculate the percentage I am aiming for off a higher base than the chart tells me I should. Everyone is a little different.
For endurance runs, it really helps me pace myself. When I was younger, I was a fairly fast runner, but never an endurance runner. My base instinct is still to go too fast, even when I should be pacing myself so I will be able to go farther. I can't tell you how many times I have lost myself and put myself on pace to burn out. You just don't realize it in the moment--without your heart rate reading telling you to ratchet it down--and by the time you do, you are done. When I am paying attention to tempo, it helps keep me at a steady pace. And even though I don't do as much interval work as I should, it can be a great tool to make sure you go hard enough and then give yourself enough recovery time. My HR monitor has even told me when when I am dehydrating and I need to drink up or when I haven't eaten enough before working out, by ruling out the possibility that I am pushing myself harder than I normally could handle. It takes guesswork out.
Feel free to PM me if you have any questions about monitors or how you can integrate one into whatever you are doing. I'm not a fitness expert, but I do have some experience using one and have found it a great help and a good motivational tool in some ways.