What could a_0=s in Shamir's secret sharing scheme represent?

What could $a_0=s$ in Shamir's secret sharing scheme represent?

As we already know in a $k$ out of $n$ secret sharing scheme, a secret is split in $n$ parts however only $k=t$ parts (of a polynomial of degree $t-1$) are needed if we want to compute the secret. Suppose that $f$ is the polynomial function such that

$$f(x)=a_{t-1}x^{t-1}+a_{t-2}x^{t-2}+\cdots+a_1x+a_0=s+\sum_{i=1}^{t-1}a_ix^i,\text{such that } s=f(0)$$

$s\in\mathbb{F}_p$, say $s=5<p=11$, but in some cases we want to encode secrets like letters etc. Could we do this with this technique?

When you are trying to do Attribute Based Encryption schemes, the collection of points has a nice property such that if you scale the x-axis by a scalar, the polynomial still passes through the same y-intercept. So, you can use this scheme to represent a hash for point combinations; and give different users an incompatible set of points (to help in collusion-resistant schemes). Points on a polynomial can be used as a sort of commutative/idempotent hash, where the original points can be discarded by pinning the curve at points x=1,x=2,...x=n.

There is a whole genre of cryptography using Kronecker Delta and secret sharing schemes; where you can encode digital circuits in equations. You can use Shamir point addition to do things that resemble things that you do with Elliptic Curves.