We have known for a long time that adhering to treatment reduces your risk of passing HIV on, but it's only more recently that we have been able to show that the risk of passing HIV on is zero when someone has an undetectable viral load.
There have been two main studies to show this. The first was done in 2016, and included 516 mixed status heterosexual couples. In all couples the positive partner had an undetectable viral load. Throughout the study, no HIV was transmitted despite there being 36,000 instances of 'unprotected' sex.
These findings were then repeated in 2018, in a study that included 972 mixed status male couples. In all couples the positive partner had an undetectable viral load. The couples had 77,000 acts of unprotected anal sex and, again, no HIV was passed on.
Combined, these two studies included 113,000 acts of condomless sex, during which no HIV is passed on. This is enough evidence to know that so long as someone has an undetectable viral load they are unable to pass HIV on through vaginal or anal sex.     

For many people the main benefit of knowing that they are undetectable will be a sense of reassurance. They no longer have to worry about passing HIV on and they can know that their health and their immune system are protected.
The undetectable = untransmittable message also aims to address some of the stigma around HIV. Once people understand that treatment can successfully suppress the virus, this will hopefully mean that they're less afraid of HIV - encouraging them to get tested and access care.
However, to make the most of these benefits, people must have good access to care. To become undetectable, people must first get tested and then start antiretroviral treatment (ART). If these services are limited people's viral loads will remain high. It's also important that people have regular viral load monitoring once they're on treatment, to confirm whether it's working properly and whether their viral load is undetectable. Unfortunately in many places access to viral load monitoring can still be very limited. Without this, people can't get the reassurance of knowing that they can't pass HIV on. However, it's important to understand the benefits of treatment anyway, as knowing the facts about 'undetectable' can encourage people to adhere to ART. They may feel motivated knowing how treatment can protect their health and health of their sexual partners.

 Re-infection is where a person who is already living with HIV becomes infected with a second, different type of HIV. This can happen if they have unprotected sex with someone living with a different strain of HIV or someone who has developed resistance to certain antiretroviral drugs. Being re-infected with HIV can make finding a treatment that works for you more complicated.
However, re-infection is not a risk if both partners have undetectable viral loads. This is because when the amount of HIV in your body is this low, you can't pass the virus on. Meaning that any resistance won't be passed on either.
To be undetectable you need to adhere to your antiretroviral treatment. You should also attend regular viral load monitoring to know that your viral load stays within the undetectable level.