At least in the linked context, an ideal (cryptographic) hash function from set $\mathcal M$ (the set of messages $M$, often the infinite set of finite bitstrings $\{0,1\}^*$ ) to finite set $\mathcal H$ (the set of hashes, often the finite set of $b$-bit bitrings $\{0,1\}^b$ ) is a mathematical abstraction. It's a random member of the set of functions from $\mathcal M$ to $\mathcal S$. It can also be modeled as a random oracle (the two are demonstrably indistinguishable). For a finite input set $\mathcal M$, we can make an ideal hash by choosing independently and uniformly at random an output element in $\mathcal H$ for each input element in $\mathcal M$. Problem with this is the storage needed grows exponentially with the bit size of message $M$, which is impractical.
Note: this is not to be confused with perfect hash and universal hash.
A practical (cryptographic) hash function is one that, for a fixed output set $\mathcal H$, can be implemented by an algorithm of size essentially independent of the bit size of message $M$, running in time linear (or near that) with that bit size, and with constant (or modest) temporary storage; yet behaves inasmuch as possible as an ideal hash function/random oracle. Ideally: for one not knowing a certain parameter of the practical hash, it is computationally impossible to distinguish the practical hash from an ideal hash/random oracle.
For a long time, the most standard way to construct practical hash functions was the Merkle–Damgård construction. If mostly does the job (in particular, has collision-resistance and preimage-reistance), but has the unwanted length-extension property: for any $M_0$ (within some huge maximum size constraint) known only by it's size and hash, one can find a short $M_1$ such that for any $M_2$ (within some huge maximum size constraint) one can compute $H(M_0\mathbin\|M_1\mathbin\|M_2)$. An ideal hash would not have that property, and there are some (few) practical cases where that matters. We now have better constructions of practical hashes, such as the sponge construction, that are computationally impossible to distinguish from an ideal hash/random oracle.
