Conditions for LL(1) grammar
Considering the above condition, should α derive a string beginning with a terminal in FOLLOW(A), then it becomes impossible to determine which derivation will be used to produce this symbol with lookahead limited to one symbol.

For instance, should $\mathrm{s}$ be the symbol that is both on FIRST(α) and FOLLOW(A), and $x$ the leftmost substring already parsed, then the following sequences are both possible:

$xA$ω $ \Rightarrow x$βω $ \Rightarrow^* x$ω $ \Rightarrow^* x\mathrm{s}$…

$xA$ω $ \Rightarrow x$αω $ \Rightarrow^* x\mathrm{s}$…ω 

Even if the grammar is not ambiguous, you can't decide which path to take by reading just $\mathrm{s}$.