You can read Mojang's official FAQ here, but here's a few more:
1. What does this mean for me?
For most people, nothing. However, if you are considered underage in your country and purchased Minecraft before 25th May 2018, you will no longer be able to play in realms unless you update your account.
2. Wait, what?
If you are considered underage in your country and purchased Minecraft before 25th May 2018, you may see this screen when trying to play on a realm. This means your parents need to provide consent to Mojang.
If this screen does not show up, it means that your account does not need further action.
2a. What is the underage cutoff for my country?
If you are an EU citizen, this would usually be your country's age of consent, typically between 13 and 16 - check this page to find out.
If you are an US citizen, the cutoff is 13, to comply with COPPA.
For other countries, the cutoff is 16.
3. I see the screen you mentioned. What can I do about this?
Very simple: Get your parent to provide consent by clicking this link. (the page looks like this)
Your parents can provide consent either by paying a $0.10, non-refundable fee with a credit card, or by signing a consent form.
The verification process is exactly the same as the one currently used to verify accounts affected by US's COPPA laws. You can read about the existing process here.
4. Is this common practice? Does Mojang make money off this?
This method of obtaining parental consent is popular amongst companies, and is the most widely used one. As processing this transaction cost Mojang more than $0.1, Mojang does not make any profit from this.
Alternatively, you can also sign a consent form and return this to Mojang, free of charge (minus printing and postage, if applicable). The form can be obtained by contacting Mojang Support. You can either post the consent form, or scan/photograph it and email it to Mojang.
5. My child has a Minecraft.net account (They use their username to log in). Can I provide consent for this account?