Why is mobile first design important?
First and foremost - laptops and desktops screens are wider than they are tall, while mobile devices are the opposite - taller than they are wide. So, a design that works well on desktop - like, for example, 3 services listed in a horizontal row, is unlikely to work on a phone. Additionally, on mobile, you have much less real estate to look at - the user sees much less of the site in any one view. Often, this means a mobile design needs less white space and more color - fonts may need to be entirely different sizes than on a computer. We also often use less text on mobile, since people rarely want to read a wall of text (or scroll forever!) on their phone.
Further, the user journey and user expectation may be very different on mobile. For example, the user may want to quickly check the hours for a coffee shop or the menu for a restaurant. For a really delightful user experience, you'll want to plan for this and make this information easily accessible and prominently displayed for your users.
Finally, the workflow is different - on a phone you are using your finger to scroll, while on a computer, you may be using a mouse. That means, on a computer, the user can hover over buttons to see if they are links, etc - this functionality won't exist on mobile, so it is important to make the workflow easy and intuitive.