What is the difference between $3$ $\frac {1}{7}$ and $3 + \frac{1}{7}$?
In the first expression, $3$ seems to be multiplied by $\frac {1}{7}$ using juxtaposition, but while doing the calculation, we don't multiply it, we add it even though there is no addtion $+$ symbol. And in the second one, it is being added, as there is a $+$ symbol.
Why do we add, if there is no $+$ sign?
In non-technical contexts, the first expression (a so-called "mixed number") is commonly used to mean $\frac{22}7$ (and would be pronounced "three and one seventh"). Many people prefer to write fractions larger than $1$ in this form since it makes it easy to see roughly how large the number is.
In mathematics, you should never use the first expression because of the potential for confusion. If you intend multiplication, write it explicitly as $3\cdot\frac17$ or $3\times\frac 17$.
[To clarify, in non-technical usage, by tradition, the standard way of writing the number is $3\frac17$ (similarly, $2.56$ means $2+.56$ not $2\times.56$). In mathematics, the standard way of writing the same number is $\frac{22}{7}$, and "mixed numbers" are not used.]