Measuring how hard you are working is a key skill for endurance training. Training by feel will likely end up with you training too hard in most of your sessions (or not hard enough).
Heart rate training is one of the easiest and cheapest ways to get started measuring intensity.
What is heart rate?
Heart rate is the number of contractions that your heart makes, usually calculated per minute (beats per minute). We can use your heart rate 'zone' to gain an appreciation for how hard your body is working. Heart rate has correlations with other intensity measures that allow us to understand how hard you are working (lactate and ventilatory threshold being two).
While it is not a perfect measure; it is good enough to get started measuring intensity.
How to go about measuring it?
There are 3 main ways that you can measure your heart rate during training sessions:
Manual pulse count
Wrist based HR monitor (built into most smart watches)
Chest strap HR monitor (fed to watch)
The cheapest way is to manually count your pulses while training but this gets cumbersome.
Since you may have already invested in a smart watch/training watch use that to measure HR instead. Adding a chest strap will make the measures more accurate than a wrist based watch (but I highly recommend using what you have right now).
We can always get more accurate later.
How do you use it in training?
Measuring and using HR are 2 very different things: a watch will measure it but you need to understand the numbers to use it well.
Using HR zones will help you understand how a specific number relates to your training impact. There are multiple domains of training where the body responds differently depending on which one you are in. The best way to do that is with lab testing, second best is field tests (which are easier to access).
What this process looks like:
Perform baseline field test (e.g. 20 min run test)
Find average HR
Estimate threshold HR
Calculate Zones
Once you have your training zones you can start to track improvements, assess training intensity and measure progress.
The biggest benefit to HR training is knowing your upper limit for endurance-based (zone 1-2 training). Most athletes train way too fast to get the benefits of easy training.