If you're not looking to read on and find out why, the short answer is yes.
But let me explain.
What is a vector?
If you google “vector”, you'll likely be assaulted with terrifying maths and physics - not the average lawyer's strong suit! Don't worry, us creatives aren't all that numerically talented either (at least I speak for myself here). I thought high school was the last I'd see of x = 2y + 8 x 39750279046, but of course I was far too optimistic.
Simply, a vector is a mathematical representation of a line. There's much more to it than that, but that's all we need to know for the purposes of making brand elements!
Just as you could take a simple data set and make a bar graph and pie chart representing the same data in different ways, so too is a vector a different way of representing a line. The curve of the line can be shown by a very long and complicated equation.
Usually, a logo will be a collection of several lines, so a vector tells you not only how each line curves, but how the different curves relate to each other.
How do you "vectorise"?
The process of vectorising is (thankfully) done by some pretty smart software and algorithms. I pop the design into Adobe Illustrator, press several buttons, fix a few curves, and voila, a series of mathematical equations worthy of Will Hunting’s approval. Once this is done, the file is downloaded as a .SVG file (this stands for Scalable Vector Graphic).
What does this mean for your logo?
Vectorising a logo or shape means that you can make it any size without losing quality.
The alternative is a simple .JPEG or .PNG. These are just images like any you take with your phone. The information is stored in pixels. Like a jigsaw puzzle, there's thousands of tiny squares with information about the colours within them. But, a vector stores the information in mathematics. When you want to recreate something, the mathematical equation doesn't change, it expands and shrinks with your needs, whereas the pixels of a jigsaw puzzle remain the same. There's only so many of them. This is why when you zoom way too far into a picture, it gets blurry. You don't want this with your logo. Nor do you want that weird glow around the logo edges when it is really small. You always want it to be clear and crisp, no matter the size.
To exemplify a different scenario, if you type something into a Word document, the text will remain clear no matter how large you make the font size. However, if you take a screenshot of some text, then make the picture bigger, it will be blurry. Why? Because the text itself is vectors - the computer is re-drawing bigger lines based on the equation, rather than enlarging pixels.
Therefore, ideally, many of your branding elements will be vectorised. It’s a good idea to start with the logo, as this is likely what you’ll use most frequently. But, if you’re thinking you’ll use your other elements to print business cards, signs, or even car wraps, you’ll want those vectorised too!