you can override templates in your theme by adding a folder with the component name in your templates folder. There you put the template you want to override.
Example: You want to overriede the template "xyz" from "block_xyz".
- Create a folder in your theme "templates/block_xyz"
- Copy the original template "blocks/xyz/templates/xyz.mustache" into your new folder.
- Change the template as you wish.
The data will be passed automatically to your template every time the template is used.